Yes. The 12 coach trains that does run via Woolwich Dockyard don't stop there.
As soon as Crossrail comes in, the freed capacity on the North Kent will mean anything more than 8 (even in Peak on the current timetable) will be overkill.
12 Car, however, for the Bexleyheath and Grove Park all-stoppers, as well as a couple of Hayes trains, is getting really "in demand" and yet only one diagram exists down towards Orpington. Absolutely appalling.
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To be honest, I don't know why King's Lynn is staying as an "Island" anyway. It would be better serviced from Liverpool Street by the Anglia franchise using the Class 379 fleet every 30 minutes.
Arrange the timetable such as there is a "Cambridge Express" from Liverpool Street to King's Lynn calling only at Tottenham Hale, Harlow Town, Bishop's Stortford, Audley End and Cambridge with a headline journey time of just over an hour (admittedly a journey time increase on King's Cross to Cambridge but made up for on the Fen line with the increase in direct journeys). Attach a Stansted Express every 30 minutes (there isn't honestly the need for it given the clientèle and how empty the trains are) calling at Tottenham Hale, Harlow Town, Bishop's Stortford and Stansted Mountfitchet; then two local Cambridge 317s, two Hertford Easts and the Stratford to Bishop's Stortford service extending to Stansted Airport to create the new direct journey opportunities.
If you are then only needing the four Thameslink departures an hour from London to Cambridge; two "all shacks" and two Finsbury, Letchworth and Royston only you can cope with the relevant demand whilst also encouraging more people to use Liverpool Street and the Crossrail connection (and for ease of getting to Stratford) with the faster trains. At peak times, use the additional two paths from Thameslink to make Ely fast trains; slowing the Cambridge fast off-peak paths slightly to include the likes of Baldock. From King's Cross "High Level", have two Royston semi-fast and two Peterborough express paths each hour.
The fleet for those can be the 23 x 377/5 which, assuming maintenance is reasonably light, can be formed up as 7 x 12 Car between 17:10 and 18:40; more than enough.
Given that the 377/2s return from Thameslink to Southern; that creates the fleet of 15 x 377/2 as well as 377/7s for West London. The 700s, including the Peak services to Grinstead / Eastbourne / Three Bridges, will get rid of a need for a lot of units formed up as 3 x 4 so the 377/5s shouldn't be sorely missed given that 9 units will come back from Thameslink.
Slide across the 36 x 376 fleet from Southeastern to Southern for the 10 Car Metro services, this frees up the 455s for other things (Coastway or South West); and permits the 40 x 365 to move to Southeastern. The 35 x 465/9 then move to Southeastern Metro. Southeastern then has a deficit; but with more units for Southern Metro there is a lower need for Southern 377/3 / 377 diagrams. I would personally move across the 30 x 375/6 units from Southeastern to Southern; and bring back the 64 members of the 377/1 fleet. I would equip them with a 375/9-style interior and then have them in a common pool alongside the 375/7 and 375/8 fleet with the "better" interior for thinner routes such as Charing Cross to Hastings and Victoria to Ramsgate / Dover. The 365s, with the lower-density layout, is suited to use on a Metro diagram as happily as Tunbridge Wells workings, Gillingham "stoppers" via Longfield and Ashford via Maidstone East.
The mathematics for the Southern franchise would suggest:
Current: 1075
- 377/1 819
- 313 762
+ 377/2 from TL 798
+ 376 1014
+ 375/6 1134
So that's a huge positive change for Southern, notably Metro.
And then on Southeastern:
Current (excluding High Speed): 1328
- 375/6 1208
- 376 992
+ 365 1152
+ 377/1 1408
A net increase of 80 vehicles; with the entire fleet (with the exception of the 375/3s which are for the likes of Sheerness, Maidstone West and in this case Bromley North) and the 466s (kept for some 10 car workings in Metro) are fit for 8 and 12 car.
The 377/5s on Great Northern have good performance for the route and supplement the 700s whilst the King's Lynn route receives key benefits including an all-day and better service (especially peak) to London using the most modern sort of stock. The 387s being built for what seems to be LOROL can transfer across to Great Western in turn once they're finished with and the electric services on Great Western for now can be formed of surplus Class 319 units for the "crap"; such as Oxford to Banbury, Newbury and the half-hourly stoppers down via Slough. They can then deflect to the North once more electrification is completed there like TransPennine.
The 317s from Great Northern can join their brothers and sisters on West Anglia along with the ex-London Overground lot (once they in turn are replaced) and all be fully-refurbished.
I think I now have Writer's Cramp.