Eurail passes are not necessarily the good deal they used to be. Especially if you can book in advance to take advantage of saver fares. Check the cost of the pass vs what you find for the individual trips to determine which is cheaper. The pass may also exclude some high speed trains.
Usually I purchase tickets from the operator in the starting city - bahn for Germany, sbb in Switzerland, trenitalia in Italy, sncf in France and nationalrail in UK.

If you are not familiar with it, this is an excellent resource for all things train related in Europe - https://www.seat61.com/

ETA - It looks like Swissair is another option for nonstop London to Zurich and seems to be consistently cheaper than BA