If the family want to travel by train here's a site where you can buy passes for the the rail network here.
https://www.visitbritainshop.com/world/travel-and-transport/britrail-passes/ depending on which one you buy you can get unlimited travel in the area of your choice, or the whole of mainland Britain. It makes Rail travel stupid cheap compared to buying tickets when they land. You must purchase the tickets prior to leaving as you cannot buy these tickets in the UK. Also I would suggest one of the party downloads the National Rail App download here...
http://www.nationalrail.co.uk/times_fares/84874.aspx so that they can plan journeys and be aware of any delays/cancellations. Visit Britain site also has some great deals and ideas.
Regardless of Silent Earth's scaremongering, London still has some of the best Museums, if they are into it. The Natural History Museum, Science Museum, and Imperial War Museum are all worth a visit and are easily in walking distance of each other. The Houses of Parliament and Westminster are also worth a visit if they are politically minded and you could get tickets for the tour etc online before you leave here....
https://www.parliament.uk/visiting/access/guidance-for-visitors-with-autism/buying-tickets/
The rest of the country is full of history and places of interest. The South West has some great scenery and history like Stonehenge and Tintagel Castle. Dorset and Hampshire are very good for non driving visitors as there is a good rail and bus service in that area. The Jurrassic Coast, the New Forest, Bucklers Hard, Beaulieu (pronounced bewley) has the stately home that housed SOE trainees during WW2, Lymington, Lyndhurst and Brockenhurst are typically picture box market towns. Heading further north, Bletchley Park is worth a visit Oxford, Olney and Woburn . Up to my part of the world, Staffordshire Potteries have a Wedgewood, Portmerion, Emma Bridgewater potteries to visit and spend money! Middleport is well worth a visit, with it's canals and Bottle kilns. Then the Peak District National Park is a stones throw away if they want a good walk in the hills.
Further North west is Blackpool(if you like commercial seasides) Morecambe and Barrow in Furness, very rugged and a bit bleak. The Lake District is just stunning and they can take the Carlisle to Settle steam train, well worth a trip. Then there's the Pennines and Yorkshire Dales with places like Harrogate (Bettys Tea Rooms is famous), Holmfirth and many other market towns. The East coast has Whitby(take the 840 bus from York for some of the best views in England on the journey through the Moors), Scarborough and then down to the wash and the Fenland and Cambridge and Ely (the highest point in the fens) Down to the south coast there's Dover, Hastings and Eastbourne.
Wales. Carmarthen and Caenarven both have great history and ancient Castles the Pembrokeshire coastal walk is stunning on a good day. Aberystwyth and Machynlleth are both worth a visit Machynlleth has the Alternative Energy Centre. There are oodles of museaums and places of interest in all of the towns I have mentioned, maybe get the Google going and see what takes their fancy.
I hope they have a great time planning and visiting. If you need any more help, just give me a shout.