Oh this bloody forum. I've spent 12 hours diddling on this and drawing out routes on top of NARA and writing out the results. It was really really long and all. Then when I click "post reply" the stupid thing throws a wobbly and loses the whole bloody lot. Fills me with the urge to defecate, it really does.
So here we go again: a tangled mix of other people's suggestions and my own chopping of it about. It's probably best to regard this as a fork of the original project beginning from post 15, because I've been too involved with working stuff out to read what was going on at the same time, and I didn't expect so much to have happened either. And I haven't looked at Scotland because NARA doesn't go north of York. Junctions/curves of whose existence I was dubious have been checked using streetmap dot co dot uk OS 1:25000 maps, which usually seem to be pretty up to date.
THE SOUTH WEST: Penzance, Taunton, Westbury, Reading, Guildford, Southampton, Bath, Severn Tunnel
WELSH LEEKAGE: Newport, Cardiff, Barry, Bridgend, Swansea district, Central Wales, Shrewsbury, Wrexham, Birkenhead, Liverpool loop
CHESHIRE AN' STUFF: Chester, Northwich, Sandbach, Crewe avoider, Stafford, Wolverhampton, Stour Valley, Birmingham New Street
BRUMMY LOOP: Camp Hill, Lickey, Cheltenham, Swindon, Didcot west curve, Oxford, Evesham, Worcester, Kiddy, Birmingham Snow Hill
GW FROM THE NORTH: Solihull, Leamington, Banbury, Wycombe, Greenford, Ealing, Acton
THE MIDLAND: Dudding Hill line, MML, Kettering, Manton, Syston, Trent
COAL WOZ ERE: Trent avoider, Earwash route, Pinxton, Kirkby in Ashfield, Shireoaks, South Yorks Joint, Doncaster, Selby
AND BACK DOWN AGAIN: Hambleton, Pontefract, Swinton, Rotherham, Beighton, Chesterfield, Derby, Trent, Nottingham, Newark
THIS BIT IS INCREDIBLY BORING: Lincoln, Sleaford, Spalding, Peterborough, ECML, Hertford loop, Thameslink tunnel
ATTACK OF THE MUTANT SQUIRRELS: South London squirrel's nest, Tonbridge, Ashford, Dover, Ramsgate, Strood, Ebbsfleet
EAST ANGLIAN CIRCUIT: Barking, Tottenham, Cheshunt, Cambridge, Ipswich, Chelmsford, Stratford, NLL
L&B: Willesden, WCML, Northampton, Coventry, Stechford, Perry Barr
CAN'T REMEMBER WHERE I'M GOING: Walsall, Sutton Park line, Nuneaton, nearly Leicester, Coalville, Burton, Lichfield
HILLS OF THE NORTH REJOICE: Rugeley, Stoke, Crewe, WCML, Carnforth, Cumbrian coast, S&C
HILLS OF THE NOT SO FAR NORTH ARE A BIT YUCK: Hellifield, Blackburn, Bolton, Manchester Vic, Todmorden, Hebden Bridge
HILLS OF EVEN LESS FAR NORTH GET QUITE NICE AGAIN: Huddersfield, Standedge, Stalybridge, Stockport, Hazel Grove, Whaley Bridge, Peak Forest loop, Chinley, Edale, Sheffield
MORE NOT COAL AGAIN: Barnsley, Wakefield Kirkgate, Normanton, Leeds, Church Fenton, York
ONWARD: To Scotland
NARA doesn't go any further north than York, so neither have I.