Firstly Interrail/Eurail passes are not usable on local buses, but generally are usable on local trains operated by Interrail partners (As long as they are taken on one of your 4 pass days)

Secondly your post is a little confusing as you show 6 legs to your trip but plan to do them in 4 days - quite a challenge since Barcelona to London needs at least 2 days (unless you are flying?).London to  Paris  is OK in a day ,and Paris - Zermat may be doable in the same day. Zermat to Milan to Venice is probably doable with no stop in Milan and Venice to Rome is easily doable in a day.

So if your plans are all by train you need at least 5 days without stops in Paris and Milan, and 2 of those would be full days of travel.

Besides this it is also a quite unthoughtful trip to make this way-try to avoid as hell double track in/out of LON. Use a planner (it wil not work yet for dec-just use a samedayofweek to get rough idea) like that of bahn.com on how long trips take and what options there are. Then replan. Lah!

I still get surprised that suddenly about any outofcontinental wants to visit Zermatt-the outer end of the line car free tiny super expensive village. Swiss has so many more similar or better places.