As background, I've been buying railway magazines for over 60 years and I inherited some which go back to the 1930s; I don't intend spending the next few days trawling through them to find specific references, but the following comments are based upon what I remember reading “somewhere” over many years!
Firstly, the Woodhead electrification; I too have wondered why so many class EM2/77 locos were originally proposed, for although I have read conjecture about a eastwards extension of the wires, I have not read anything specific. However, I have read that the original plan envisaged electrification to Manchester Central as well as London Road (as it then was).
If you look at how “generous” the LNER/BR was when electrifying connecting lines to the route in the Manchester area, this makes sense from a freight perspective; just west of Throstle Nest was Manchester Docks and the Trafford Park Industrial Estate, the former was a major British port at the time, and the latter included a steel works. That part of Manchester was thus a major destination and starting point for freight traffic, and to be able to reach it without a change of locomotive seems eminently sensible.
There weren't any clearance issues with electrification of the Woodhead Tunnel so far as I am aware – in fact, photos exist showing electrification gantries installed at the Woodhead end; the new tunnel was bored because of the condition of the old tunnels – I remember reading a report which implied this was the cheaper option, the old tunnels were so bad. However, there were clearance issues at Thurgoland, and this was addressed by driving a new westbound bore and singling the track through the old one.
As for the London extension, Francis Douglas Fox was the resident engineer for the southern section, and his presentation to the Institution of Civil Engineers (Paper no 3209) was available online, but a quick search whilst writing this hasn't thrown it up. Fox states that the maximum gradient allowed was 1 in 176, and apart from one curve of 60 chains radius (he doesn't say where at), “the normal curve” was of one 1 mile radius; he describes these as “severe restrictions” on construction and resulted in some major embankment and cutting works, and were due to “the Company's resolve to secure a first class running line, as direct as possible, and with easy curves and flat gradients, so as to admit of high speeds”. What were classed as high speeds isn't stated, but in Tuplin's book 'Great Central Steam' there is a report of a run behind a 'Director' on a Marylebone – Manchester express, first stop Leicester, which averaged 63mph between Aylesbury and Leicester; it went through Whetstone at 80mph! The date of the run isn't stated, but he quotes the loco's GCR number (510, 'Princess Mary'). Overall time was 105.7 minutes for the 103.1 miles between London and Leicester; not bad for a 4-4-0 pulling 290 tons.
So what would have been possible with modern traction?
There was an article in 'Rail' some months ago by Gareth Dennis and it included a table which suggested that the maximum speed on the GC line would have been 115mph (if I remember correctly); presumably, this was based upon Network Rail's present standards, and as I'm not a permanent way engineer, I've no idea if any form of derogation is possible to permit higher speeds. However, I remember seeing a speed/curvature graph produced by Adtranz in Sweden in connection with the Swedish X2000 tilting train, and what stuck in my memory was that it showed a non-tilting train could do 200kph on a curve of just over 1500m radius; consequently, I've always associated a curve of 1 mile (just over 1600m) with 125mph.
The 'InterCity Story' includes (on page 87) a map of the 1989 proposal for a new high speed line to relieve the WCML; the option 1 route seems to follow the line of the GC between just north of Aylesbury and near Rugby. And the late Adrian Shooter's book on Chiltern includes a “might have been” section which covers their plans to reopen the GC main line as far north as the Leicester area, connecting into the MML near Wigston; this was for a 125mph railway, and the proposal included some deviations from the original route at Brackley, Woodford Halse, and Rugby. The consultants engaged concluded that this was doable and the business case developed suggested that it was affordable, but Chiltern decided to concentrate on the Birmingham route and return to it later; however, by the time they were ready to do that, HS2 was being developed, and that meant that the Chiltern project couldn't be delivered because of conflicts at certain places between its route and that proposed for HS2. Finally, the work done by Atkins in 2010 regarding alternatives to HS2 includes a graph of potential maximum speeds on the GW&GC Joint based upon alignment; the quality of the online pdf isn't very good, but it seems to show that parts of it have a theoretical maximum of 300kph/186mph.
So based upon the above, I think it can be concluded that the GC and GW&GC Joint had the potential to provide a faster route to London from the East Midlands than via the MML; but you have to remember that very few people travelling to London end/start their journey within a few minutes walk of either St Pancras or Marylebone, and consequently the journey time gain to/from London could soon be lost by Marylebone's poorer connectivity for onward rail/bus/underground journeys. Perhaps this could have been overcome by building a connection between the GC and Midland lines where they are close just north of Belsize Tunnel – at one time, only a railway owned coal yard separated them – but that would have been challenging as Underground tracks are also between the two lines
If the GC main line had lasted longer as a passenger route, it's very unlikely Chiltern's proposals would have been adopted by BR; they were based around park & ride stations at Brackley, Daventry, and Lutterworth (close to M1 junction 19), and the business case relied upon abstracting traffic from both the MML and the WCML!
I think it's reasonable to conclude that, back in the mid/late 1950s, BR envisaged a long term future for the GC main line, but as a major non-passenger route; consequently, it made sense to get rid of the Marylebone expresses. Moreover, the London end was viewed as a branch, the main trunk being Annesley – Woodford Halse – Banbury/Cheltenham (via the SMJR and the connection built with the GWR near Stratford Racecourse). This conclusion is based upon a few reports/articles in 'Trains Illustrated' (as 'Modern Railways' then was)
One report picked up on a comment made by a LMR manager during a talk, I think about the WCML electrification; the gist of it was that connections were going to be made with the GC main line (no locations were mentioned) and that parcels traffic would be transferred to it from the WCML and MML. With regard to timescale, it was to be after the electrification programme was completed as the LMR didn't have the resources to take on the two the projects at the same time.
The second source for the conclusion is a lengthy article also in 'Trains Illustrated' about freight on the GC main line.
I think the primary reason for the construction of the link at Stratford-upon-Avon between the SMJR and GWR (together with the work at Fenny Compton) was to speed the flow of iron ore to South Wales; a major source of ore was the Oxfordshire Ironstone Co facility near Banbury, and I guess its traditional route had been via Leamington Spa to Stratford. However, the connection also shortened the route between Woodford Halse and Cheltenham via the SMJR, cutting out the need to go via Broom and then the MR route towards Bristol.
According to the article, BR had been experiencing problems for some time in the Birmingham area regarding recruitment and retention of staff, and so a plan was hatched to avoid the West Midlands completely for freight traffic flows wherever possible. Using the connections between the GC and MR in South Yorkshire, traffic would then flow to Woodford Halse, and then via either the SMJR and the new connection to South Wales, or to Banbury if heading to Southampton and other parts of the GWR network. Woodford Halse crews worked over the SMJR and new connection to the GWR, but I don't know how far south west they went (there was a photo published in 'Trains Illustrated' of a Woodford L1 tank and brake vans on a crew familiarisation trip on the new connection at Stratford).
I can't recall how many freight trains were operating north of Woodford, but I do remember thinking “that's a lot!” Certainly, the article intimated that the GC main line was busy with freight, and that it was expected to remain so.
A few other bits.
According to Dow (in his Great Central trilogy, volume 2) the Acts of Parliament authorising the construction of the GC main line through Rugby included a connection with the LNWR Peterborough line near Clifton Mill; the constructed route was authorised by an 1894 Act, the original one – in 1893 – proposed a route more to the east and so it would have been further from the town centre.
The MS&LR (as it then was) must have been talking with the GWR about the GW&GC Joint before its London extension was completed, as the existing GWR line between High Wycombe and Princes Risborough was taken over the the GW&GC Joint Committee in 1899, the same year as the GC main line opened (see 'Britain's Joint Lines' by HC Casserley, page 95).
And when St Pancras was built, a second tunnel was constructed alongside the Metropolitan Railway to allow the Widened Lines to be extended westwards (I think it's now used for the eastbound platform for the Circle/Met line); this could have been used if Watkin's vision of trains under the channel had come to pass.
And going back to the original question, the log in Tuplin's book is of the 15.20 Marylebone – Manchester; extra coaches were added at Leicester (load 330 tons) and it did the 23.4 miles to Nottingham Vic in 24.57 minutes, and then the 38.2 onwards to Sheffield Vic in 45.28 minutes. Obviously subsidence wasn't a problem in the Derbyshire coalfield – it went through Staveley at 90! No idea what comparable MR journey times were in the early twentieth century, but the Leicester - Nottingham and Nottingham - Sheffield ones would still be acceptable today
Sorry to have rambled on!