This is an interesting question. I fully intend to travel over the entire network, but am yet to do so. I have however travelled over all currently open passenger lines in the vicinity of the North West, including all diversionary routes and curves as far north as Windermere/Hellifield/Carlisle except for Rose Grove - Colne, Hyde - Romiley/Rose Hill, Hazel Grove/New Mills Central - Sheffield, the Manchester Airport South Curve, Dinting - Hadfield avoiding Glossop and the Furness/Cumbrian Coast and I have also made quite a dent in the network in Yorkshire and the West Midlands and have done the entire Manchester Metrolink.
I'm in danger of falling behind though - eg the flyover at Hitchin.
I've recently done the original Crossrail (Paddington to Abbey Wood) but now lack the new east/west connections.
I've done the new LO Barking Riverside branch, but am missing the Northern line's Battersea Power Station extension.
Shan't bother with West Mids Metro until there is a full service to the new extremities (Five Ways and Wolves station).
I only learnt of the Down Cambridge Flyover’s existence yesterday!
I ventured to Okehampton on opening day, travelling to Exeter St Davids via the Halton Curve, Chester, Crewe, Newport and Weston-super-Mare and then returned avoiding Weston-super-Mare on a CrossCountry HST changing at Tamworth instead of Birmingham New Street.
During a first trip to London this year, I managed to do the WCML south of Nuneaton (but not the Northampton loop) and the most central sections of all Underground lines and the DLR except the Northern and Metropolitan, which I didn’t end up going on at all.
I had already been as far as Rugby via Willenhall and Aston, doubling back to Coventry during a diversion.
Then during a second trip to London on the Crossrail opening day I travelled on the CrossCountry service to Reading, including my omissions through Wolverhampton and between Proof House Junction and Stechford, before doing all Elizabeth Line services from Reading - Paddington, Paddington - Abbey Wood and Liverpool Street - Shenfield fast on a 720, returning on a 315. I did this without staying overnight and got the first train I could from Paddington having started on the second train from Southport and who should be on board but none other than Geoff Marshall! Unfortunately the lines between the GWML and GEML tunnel portals, Paddington and Whitechapel were not yet open and I ran out of time to do the Battersea Power Station Station branch, only getting as far as Kennington before having to return to Euston.
Another day I decided to do the TPE diversion from Manchester Piccadilly to Sheffield via Huddersfield during a Hope Valley blockade, including Crofton West Junction - Hare Park Junction, a 20mph section of track that feeds directly into the ECML and intended to return via Penistone, until I realised it was the last day of the Class 317 on Hertford East - Liverpool Street, so instead went from Sheffield - Doncaster via Rotherham Central (having avoided it on the way) and did a big chunk of the ECML to Stevenage and Hertford North, walking across Hertford town centre to the other station, but this was all in the extreme heat this summer, which was noticeably hotter in the south than in the north and the 317 was the first train other than a 769 early in the morning that I’d been on all day without air conditioning! Upon arrival at Liverpool Street I found that the Elizabeth Line service had collapsed, so instead used the Metropolitan Line for the first time to reach Farringdon to change for Thameslink to Blackfriars, so I could decide how to get home with a view of the Thames. I decided to attack half of the Midland Main Line, changing at Luton, Kettering, Leicester, Nuneaton and Stafford, to do a variety of rolling stock. A 4 car 360 with broken air conditioning was particularly unbearable, until I arrived at Nuneaton after almost missing all connections, only to realise that the WCML was now closed due to a lineside fire started by the Duchess of Sutherland and had to pay over £50 for a taxi just to Rugby, which I luckily managed to claim back from LNWR.
I have also made a fourth trip to London where I travelled from Manchester Piccadilly and did Macclesfield - Colwich via Stoke-on-Trent but not Stafford and this time I did manage to do the Battersea Power Station Station Branch, having reached there using the Uber boat by Thames Clippers, but with only 10 minutes to spare once I got back to Euston.
When I know I want to use all lines at some point, it can be easy to start filling them in with pure chaos and then it becomes possible to find the most efficient way to do the rest. There are also some interesting combinations of track rolling stock such as Pendolinos via Chat Moss, Castlefield or Bolton, 720s through Seven Sisters or the daily IET from Banbury. I am trying to work out the most efficient way to do the London, Tilbury and Southend lines including the line from Romford - Upminster and the links to Stratford and Liverpool Street, but first I’m more likely to do some of the lines from Waterloo where I’m more likely to find a 455/7 since I’ve never even scratched the Southern region unless Blackfriars and Okehampton count (the AC platforms at Abbey Wood do not!) and I would like to do the other half of the boat trip to Barking Riverside and do that line.
I don’t know what the best way to do the GWML would be since London - Bristol isn’t exactly a useful journey to me if I was to travel to either London or Bristol, but as for the European railways, I note that some including the SNCF have a full geographic network map on their website, while others (such as ours) do not, leaving us to rely on things like Apple Maps and Rail map online.
