Last summer, most of Europe experienced a record-breaking heat wave and drought. When we flew into London near the end of July, the normally-green landscape of the English countryside was brown. Amsterdam was uncomfortably warm. Even in the Swiss Alps it was warm for serious hiking. The heat wave broke in August; in the Alps (Chamonix) we experienced 2 days of massive downpours which were welcomed by the locals, but not fun for hikers.
Of the places on your list, I would definitely include London and English countryside ( add York and maybe Scotland), and the Lauterbrunnen area. We had an apartment in Mürren the first week of August and it was perfect. The über-expensive aspects of Switzerland are hotels and Restaurants. If you can rent an apartment and cook "in", it is not bad.
If your visit can include the first weekend of August in Mürren, you will be there for the village festival and parade. Well worth planning around. I would recommend our apartment to you, but it is larger (3bdr.) and thus more expensive than you need. The apartment at Chalet Fontana is moderate in price and would serve well. We have stayed there as a family of four several times.
http://www.ferntree.ch/chalet/fontana_summer.htm
The grocery store ( Coop) is practically across the street ( pedestrians only), and the price of groceries is reasonable.
London is pricy as well, but there again if you can rent a flat you can keep the costs down. We spent 3 weeks there with our kids and grandkids recently. The flat was on the expensive side, but groceries actually cost less than we would pay in the US for the same high quality. (Note, this may change after Brexit). Life is less expensive in the countryside and small towns.
The key to keeping trip costs down, in my view, is to limit long travel transfers. A compact trip is less expensive and more comfortable than one that goes all over. If this were my trip, I would plan two weeks in the U.K. and one in Switzerland, flying into London and out of Zurich.
If you want to move around a bit more, northern Italy would be the logical choice. Fly into London, then from there to Zurich; spend 5-6 days in Switzerland, then take the train to Milan and spend another 5-6 days in Italy. It you have already been to Lake Como, and I would never go to Venice in the summer. So maybe people can suggest somewhere else in Italy that makes sense. But personally Inwould stick to the U.K. And SwitzerlNd in your time frame.