Take one of the comfortable daily trains from London’s Paddington Station to the Cotswolds (stations Cam & Dursley, Cheltenham, Gloucester, Kemble, Moreton-in-Marsh, Stonehouse, Stroud or Ashchurch), and arrive as soon as one to two hours later.
If you are looking for more of a budget-friendly option to get to the Cotswolds then take the bus from Victoria Coach Station in London. Stops in the Cotswolds are Cheltenham, Gloucester or Stroud. It will take between 2,5 and 3,5 hours to arrive, but will cost significantly less than the train. Busses are comfortable and air conditioned. Be aware that the Cotswold Way is a linear walk, and that you need to get back by yourself at the end of the route.
The Cotswold Way is an easy to medium hike that can be done by any level of hiker. Most of the route is easy, with occasionally some steep ascents and descents, but since the total ascend is only 317 meters above sea level, this is nothing to be worried about.