We've been looking at a Brit Pass for touring from London to Edinburgh by way of Bath and the Cotswolds. It would seem that lodging in Moreton On Marsh is all outside the village proper. Is that correct? Are there rooms to be had in that village?
Rick Steves guidebook has some b&B listings.
Not sure what your overall plan is but personally I think a car is necessary to make the most of your time in the UK, and get to places not easily accessible by public transport.
Train to Salisbury and pick up a rental car for a week
Salisbury - Bath - Cotswolds - Oxford - Stratford - Peak District - York
Drop off your rental car in York and then train to Edinburgh
If you don't have Rick's guidebook and other hotel searches are not giving you a narrow geographical focus, then search for "B&Bs near Moreton-in-Marsh" on Google Maps and you can see options well by location.
I used the Trip Advisor website in conjunction with RS guidebook to choose our lodging. Sometimes the ones in Rick's guide are booked but they are often reviewed on TA so one can choose something with comparable reviews. Do be careful that you check the actual location of the B&B's as TA sometimes lists ones that are actually a bit out of town.
There's no mention of the dates you are looking at but booking.com shows 4 or 5 places directly in Moreton-in-Marsh and airbnb.com shows 2. There are many many more within 5 and 7 kilometres. Some of those might pick you up from the train station, possibly at no cost or for a fee. As mentioned previously a rental car is a great asset in this area.
There are a few places to stay in Moreton-in-Marsh. It has been a while since I've visited there, but i always liked the location for exploring the Cotswold region. As previously mentioned, having a car is best to tour the area.
Alastair Sawday's website www.sawdays.co.uk is a good source. Doing a search for Moreton-in-Marsh returned 10 B&Bs. There are also Inns and hotels listed. The site normally lists the more up scale B&Bs.