I think there are two approaches you could take.
1. Rent one place for 2 - 3 months. The north Cotswolds would be best because it would be closer to Worcester. Or you could look closer to Worcester. The Malverns, south-west of Worcester, is a lovely area and may have better transportation links to Worcester.
2. Rent a few different places. Maybe one month each in three places? Or give yourself a few weeks at the beginning to travel to different parts of the UK and then settle into one place for the rest of the stay.
Option 1 gives you the opportunity to live in one place and see what it is like living in England. But if you are aiming for April - June 2015, some vacation rentals may already have some weeks booked. You may end up with Option 2 just because you can't find something available for the whole time. If you are looking at 2016, you have plenty of time and will easily find something you can book longer term.
I think you will be looking for a vacation rental (called holiday cottages in the UK) because that will be the best source of a furnished short term rental. You should be able to get a discount because you will be renting for more than one week, but June is getting into the popular season when they are more expensive.
I have a list of vacation rental resources for the Cotswolds on the site:
http://www.sloweurope.com/vacationrentals/england/gloucestershire/
Dealing directly with an owner via homeaway.com or one of the other rent from owner sites may get you a better deal.
You could also look at something like sabbaticalhomes.com to find something less expensive.
Public transportation in England is not as good as it should be. Trains are expensive, local bus service has been cut back. When considering a place to rent, look at the transportation available.
www.thetrainline.com shows train service for the whole country.
www.travelinesw.com shows buses and trains for the southwest.
Read through some of the threads in this forum.
@Lisa in Ottawa is at the end of a three month stay in Oxford and has been posting about her experience.
Keep us posted with your plans. When you get to the point of looking at different locations, I would be happy to give my opinion.
