Well, from a fresh start, we'd need to start with a simple, baseline network. I'd start by building a London superstation, with 60 platforms in a circular arrangement - six for each of the ten service groups:
Anglia - largely mirrors the real-world GEML, with stations at Ilford, Chelmsford, Colchester, Ipswich, Stowmarket, Diss and Norwich.
Anglia Commuter - a hybrid between the current C2C and Crossrail, operating slower services to Colchester via Southend - stations at Canary Wharf, London City Airport (which in this alternate world has subsumed the dock and acts as a budget airport), Barking, Rainham, Grays, Basildon, Wickford, South Woodham Ferrers, Maldon, Tiptree, Marks Tey and Colchester. 100mph linespeed.
Kent - operating the commuter lines from Kent. Stations at Dartford, Gravesend, Chatham (Medway Parkway), Maidstone, Ashford, Folkestone and Dover.
Hampshire - services to the South Coast. Stations at Croydon, Guildford, Alton, Winchester, Southampton, Brockenhurst, Bournemouth and Weymouth.
Devon and Cornwall - services to the far reaches of the country. Stations at Slough, Bracknell, Basingstoke, Andover, Salisbury, Blandford Forum, Yeovil, Chard, Honiton, Exeter, Newton Abbot, Totnes, Plymouth, Bodmin, Truro and Penzance.
Wales - services to Wales. Stations at Slough, Reading, Newbury, Swindon, Chippenham, Bath, Bristol, Newport, Cardiff, Bridgend and Swansea
Lancaster - services to the North West and Scotland. Stations at Watford, High Wycombe, Oxford, Banbury, Leamington Spa, Coventry, Birmingham, Wolverhampton, Stafford, Stoke, Crewe, Northwich, Warrington, Wigan, Preston, Lancaster, Kendal, Penrith, Carlisle, Dumfries, Kilmarnock, Glasgow, Stirling, Perth and Dundee.
Northamptonshire - the slower, commuter services connecting to Coventry on the Lancaster services. Stations at Edgware, Watford, St Albans, Luton, Leighton Buzzard, Milton Keynes, Northampton, Rugby and Coventry.
Yorkshire - Services to Yorkshire, mirroring the Midland Mainline. Stations at Luton, Bedford, Kettering, Leicester, Loughborough, Nottingham, Mansfield, Sheffield, Barnsley, Wakefield, Leeds and York.
Lothian - largely a mirror of the current WAML and ECML. Stations at Stansted Airport, Cambridge, Peterborough, Grantham, Lincoln, Doncaster, York, Darlington, Durham, Sunderland, Newcastle, Berwick upon Tweed, Dunbar, Edinburgh, Dunfermline, Perth and Dundee.
All of the services will operate on mid to highspeed electrified lines, running at a maximum speed of 150mph (about 240kmph). The stock will be double deck for maximum capacity.
In addition to this, there will also be an outer London circular railway, maintaining an average distance of 30 miles outside the capital. This will operate a maximum speed of 100mph.
Other large cities, such as Manchester, will have developed their own suburban railway networks and metros, and as such, are not the focus.
Ticketing would be much simplified in this universe, considering most major services operate from the London Superterminus. A flat rate of 40p per mile travelled, or 60p in First Class. And it'd all be controlled by one national entity.