Hi Norma
A lot depends on how you are travelling. B + B requires a different strategy to camping. If you are B + Bing, you may have to book in advance, though May is probably low season. Others will be able to comment more authoritatively on this. I have walked the West Highland Way, the Cotswold Way, and the South Downs Way doing wild camping. The great advantage of wild camping is that you can go just as far as you like every day. SDW and WHW were easy, with many suitable tent spots. The Cotswold Way was more difficult, but still worked out. The disadvantage of camping is weight. However, I found that with tent, sleeping bag, food and clothing, I was able to get my pack weight down to 13 kg. On the WHW (the first LD trail I did) I carried 22 kg and really suffered. As John says, keep the weight to an absolute minimum. If you are B + Bing, you can wash clothes at night, and hang them over your pack during the day to dry while you walk.
Food: you will be astonished at how little you eat. I found that 200g cheese and 200g dates (all I carried for food) per day was too much. I had to force myself to eat. A piece of fruit every day is pleasant. After the WHW I never carried a stove, and having everything cold was not a problem. Hot tea and hot soup is nice, but not at the cost of lugging an extra pound and a half or two pounds on your back for 200 miles.
Your biggest problem may be water. Long distance trails, by their natures, stay away from towns. The Cotswold Way goes through a few villages, but on one day I had to ask for water from a pub, and on another from a tea room (it was Sunday and all the shops were shut).
Your route: The Mendip Way ends a long way from the North Downs Way, which starts in Farnham. If you went up the Cotswold Way from Bath to near Stroud, then went east, you could reach the Thames Path near Kemble. The Thames Path will take you right across England, and has the great advantage of a lot of water points. Most lockhouses have outside taps for the riverboats (run the water for a while before filling your bottle.) Camping could be a problem, especially in the lower reaches. There are a few official campsites. All my walking on the Thames Path has been in day walks, so I have not considered it from an accommodation point of view. From Weybridge on the Thames Path you could go south down the Wey Navigation to Guildford and join the North Downs Way. I have walked the NDW in day walks as far as the Medway, and I think with careful planning you can get enough water every day. South of the Medway is terra incognita to me, but it looks pretty straightforward.
Daily distances: this is really a matter of personal choice (and the weight of your pack). If you walk with the LDWA, you should be able to put away 25 miles a day comfortably, day after day, provided your feet hold out. On multi-day walks I find that I feel shattered after the first day, really shattered after the second day, but on the third and subsequent days, I can walk from dawn till dusk at a good pace, and it is only the deteriorating condition of my feet which slows me down.
Hope this helps
Elton
