Hi -
All the above is relevant and should noted, but for a three-four day walk that gives you what you seem to be after I'd suggest the Ridgeway National Trail, or to be precise, half of it! I'd start at Goring and Streatley and walk towards Avebury, which is the reverse of the usual direction, but at least has the advantage of taking in ancient sites - earthworks, ancient settlements, Uffington White Horse, Waylands Smithy, etc. You could detour a little bit at the end of the walk to West Kennet Long Barrow, and Silbury Hill and conclude your walk up the stone avenue into the always stunning Avebury. As a village occupies part of the stone circle by booking well in advance you can spend the night there - wonderfully atmospheric.
There are also a number of pleasant villages and towns that offer accommodation on, or just off route. Although when we stayed in Wantage we rang for a taxi to take us there and back. The main problem is in the event of hot weather (does happen occasionally!) the Ridgeway is above any water sources in the most part, so carrying plenty with you is a must.
As a National Trail the Ridgeway, often dubbed 'England's oldest road' is well signed and maintained, has a dedicated website and any number of guide books and maps. Getting to the start, which is on the Thames is relatively easy from London by train, getting away would be by infrequent bus to and via Swindon for rail links to all points.
As a northerner I am compelled to give a shout out to my local trail The Dales Way (or the Nidderdale Way, or even the Six Dales Trail) but while they offer sometimes strenuous walking in remote areas, they may not offer the Neolithic type of sites I believe you are after.
Wherever you end up walking I'm sure there will be something that you'll enjoy and you have a proliferation of trails, tracks and paths to choose from, one of the great benefits of the U.K. Though I say so myself!
Happy Trails - hope you have a great time!
Ian
PS. You could also do three or four days on the six hundred mile plus South West coastal path (a national trail) which many visitors from across the pond seem to like to do. Although I've not walked it (it's on the list!) a company I used recently seems to specialise in it, Encounter Walking Holidays. They'll supply you with all the necessary maps and guides and will probably recommend which part(s) of the path might best suit your purpose book your accommodation and arrange for your main luggage to be transferred to your digs each day.. You can read plenty of reviews which might also help at www.encounterwalkingholidays.com