As part of other 'work' I am doing, I have reformed a list on WikiPedia of Operational Standard Gauge Heritage Railways in the UK^▸ (United Kingdom);  I have sorted them - first those which are (for definite) in GWR^▸ (Great Western Railway) franchise (or should I call that management) territory (+) , those of which are neighbours (,) and those which are far, far away or feel it (-).

Missing from the original list (should I include them) - Didcot Railway Centre, Crich Tramway Museum, Great Orme Tramway, Downpatrick and County Down Railway, Fort William to Mallaig ... all of which could argue for place, or feel hard done by for failing the criteria.

+ Avon Valley Railway, Bitton, Gloucestershire
+ Bodmin & Wenford Railway, Bodmin, Cornwall
+ Bristol Harbour Railway, Bristol
+ Cholsey & Wallingford Railway, Wallingford, Oxfordshire
+ Dartmoor Railway, Okehampton, Devon
+ Dartmouth Steam Railway, Paignton, Devon
+ East Somerset Railway, Cranmore, Somerset
+ Gloucestershire Warwickshire Railway, Toddington, Gloucestershire and Broadway, Worcestershire
+ Helston Railway, Prospidnick, Cornwall
+ Plym Valley Railway, Marsh Mills, Devon
+ Somerset & Dorset Railway, Midsomer Norton, Somerset
+ South Devon Railway, Buckfastleigh, Devon
+ Swindon & Cricklade Railway, Blunsdon, Wiltshire
+ West Somerset Railway, Minehead, Somerset

, Barry Tourist Railway, Vale of Glamorgan, Glamorganshire
, Bluebell Railway, Sheffield Park, Sussex
, Cambrian Heritage Railways, Oswestry and Llynclys, Shropshire
, Chinnor & Princes Risborough Railway, Chinnor, Oxfordshire
, Dean Forest Railway, Norchard, Gloucestershire
, Fawley Hill Railway, Buckinghamshire
, Gwili Railway, Bronwydd Arms, Carmarthenshire
, Isle of Wight Steam Railway, Havenstreet, Isle of Wight
, Kingfisher Line, Titley, Herefordshire
, Llanelli and Mynydd Mawr Railway, Cynheidre, Carmarthenshire
, Llangollen and Corwen Railway, Llangollen, Denbighshire
, Mid Hants Railway, The Watercress Line, New Alresford, Hampshire
, Pontypool & Blaenavon Railway, Monmouthshire
, Rowden Mill & Fencote Railway, Herefordshire
, Severn Valley Railway, Bridgnorth, Shropshire
, Swanage Railway, Swanage, Dorset
, Telford Steam Railway, Horsehay, Shropshire

- Alderney Railway, Alderney
- Aln Valley Railway, Alnwick, Northumberland
- Battlefield Line, Shackerstone, Leicestershire
- Bo'ness & Kinneil Railway, Bo'ness, Falkirk
- Bowes Railway, Tyne and Wear
- Caledonian Railway, Brechin, Angus
- Chasewater Railway, Staffordshire
- Chatham Historic Dockyard Railway, Kent
- Churnet Valley Railway, Cheddleton, Staffordshire
- Colne Valley Railway, Castle Hedingham, Essex
- Derwent Valley Light Railway, Murton, North Yorkshire
- Doon Valley Railway, Dunaskin - Waterside, East Ayrshire
- East Kent Railway, Shepherdswell, Kent
- East Lancashire Railway, Bury, Greater Manchester
- Ecclesbourne Valley Railway, Wirksworth, Derbyshire
- Eden Valley Railway, Warcop, Cumbria
- Elsecar Heritage Railway, South Yorkshire
- Embsay and Bolton Abbey Steam Railway, Embsay, North Yorkshire
- Epping Ongar Railway, Ongar, Essex
- Fife Heritage Railway, Leven, Fife
- Foxfield Light Railway, Blythe Bridge, Staffordshire
- Great Central Railway (Nottingham), Ruddington, Nottinghamshire
- Great Central Railway, Loughborough, Leicestershire
- Keighley & Worth Valley Railway, Haworth, West Yorkshire
- Keith & Dufftown Railway, Dufftown, Banffshire and Keith, Morayshire
- Kent & East Sussex Steam Railway, Tenterden, Kent
- Lakeside & Haverthwaite Railway, Haverthwaite, nr Staveley, Cumbria
- Lavender Line, Isfield, East Sussex
- Lincolnshire Wolds Railway, Ludborough, Lincolnshire
- Mid Suffolk Light Railway, Brockford, Suffolk
- Mid-Norfolk Railway, Dereham, Norfolk
- Middleton Railway, Hunslet, West Yorkshire
- Midland Railway, Butterley, Derbyshire
- Nene Valley Railway, Wansford, Cambridgeshire
- North Norfolk Railway, Sheringham, Norfolk
- North Tyneside Steam Railway, North Shields, Tyne and Wear
- North Yorkshire Moors Railway, Pickering, North Yorkshire
- Northampton & Lamport Railway, Pitsford and Brampton, Northamptonshire
- Northants Ironstone Railway, Hunsbury Hill, Northamptonshire
- Peak Rail, Matlock, Derbyshire
- Ribble Steam Railway, Preston, Lancashire
- Rother Valley Railway, Robertsbridge, East Sussex
- Royal Deeside Railway, Milton of Crathes, Aberdeenshire
- Rushden, Higham & Wellingborough Railway, Rushden, Northamptonshire
- Rutland Railway, Cottesmore, Rutland
- Spa Valley Railway, Royal Tunbridge Wells, Kent
- Stainmore Railway, Kirkby Stephen, Cumbria
- Strathspey Railway, Aviemore, Highland
- Tanfield Railway, Marley Hill, County Durham
- Waverley Route Heritage Association, Whitrope, Roxburghshire
- Weardale Railway, Stanhope, County Durham
- Wensleydale Railway, Leeming Bar, North Yorkshire
- Yorkshire Wolds Railway Restoration Project, Sledmere–Fimber, East Yorkshire

Grahame, I think you could include the Chinnor & Princes Risborough Railway in your first GWR^▸ (Great Western Railway) group as that is its ethos, notwithstanding more modern diesel motive power and some guest stock. Its steam, coaches, stations and signalling are all GWR/WR. Granted, Princes Risborough North 'Box was a GWR Joint company build.

Are these all standard gauge: Crich Tramway Museum, Great Orme Tramway, Downpatrick and County Down Railway? Does the Irish gauge count as standard?

Not sure if it counts, as its not on a legacy formation, but Beamish has a short running line at Std gauge plus a separate set of rails at the mining area