I think using the train in Britain to get to interesting places, and to see the landscape in between, is much the best idea (as compared with car or bus). Personally, I prefer to book my own travel and accommodation, rather than being stuck with an itinerary designed by someone else.
So, assuming you would be flying into London, I would book a few nights in or near London to see the sights in or near London that interested me. Some famous destinations - Oxford, Cambridge, Ely, Canterbury and Salisbury for example - are easy day trips from London (journey times of under 90minutes each way). Same-day return train tickets for these destinations can be bought anytime before travel and do not require reservations and (subject to the exclusion of some peak-time trains) enable you to travel out and back on any train on the chosen day. For some of these destinations, it is possible to make a modest saving by buying "Advance" tickets (this is a type of ticket, and restricts you to travelling on the particular train(s) you reserved when booking - flexible tickets bought in advance are not "Advance" tickets) but for these destinations the saving is often not worth the loss of flexibility.
For travel further afield, it is possible to make considerable savings by booking "Advance" tickets. On any particular route, the cheapest Advance tickets are sold first, so it is useful to know that tickets are usually released for sale about 12 weeks ahead of travel.
For example, London to York takes 2 hours by train. York is a great place for a 2-day visit with an overnight stay, but equally is possible as a day-trip from London.
There are as many views about the most scenic British rail routes as there members of this Forum: some would vote for the journey down to Cornwall in the South West (particularly the section of line between Exeter and Plymouth), others for the section of line from Newcastle in North East England to Edinburgh in Scotland, others for the line from Shrewsbury through Wales to Swansea, others for the line from Newcastle-upon-Tyne to Carlisle (get off at Hexham for the town itself and local buses/taxis to Hadrian's Wall), others for the line from Settle to Carlisle (which is part of the scenic route from York to Glasgow or Edinburgh - stop off between Settle and Carlisle for rural upland England), others for the line from Edinburgh to Dundee (stop off at Leuchars for a shuttle bus to St Andrews), others for the line through the mountains from Glasgow to Fort William, and then to Mallaig for the ferry to the Isle of Skye (from Skye there are ferries to the Outer Hebrides islands of Lewis and Harris, and there is the road-bridge back to Kyle of Lochalsh for a train on to Inverness and mainline connections south and north), and others for ....
Some forum members have an interest in preserved (often steam-train operated) railways, so would use the national rail network to reach a preserved line (e.g. Grosmont on the line to Whitby to interchange with the North Yorkshire Moors Railway).
Others use the national rail network to escape to the countryside: Windermere station for the Lake District, Thirsk or Grosmont for the North Yorkshire Moors, Northallerton for Wensleydale, Darlington for Richmond (Yorkshire) and Swaledale, Moreton-in-Marsh for the Cotswolds, Knighton for Offa's Dyke, Matlock or Edale for the Peak District, "Hoveton & Wroxham" for the Norfolk Broads, Berwick-on-Tweed for a bus-link to Lindisfarne (aka Holy Island and separated from the mainland by a causeway covered by water at high-tide), and many many more.