Do you wear a big cape and have "S" on your t-shirt? Yes - maybe, in a push.
Tower of London is exhausting and at least half a day. Expensive too.
Cabinet War Rooms, old name, Churchill War Rooms or some such new name, is a one hour queue if you are lucky and probably 3 hours if you go quickly - expensive and not easy to get into so you will want your money's worth.
Westminster Abbey is at least an hour queue and at least 2 or 3 hours inside if you move quickly. Expensive too, so you will want your money's worth.
By the way - there are a few attractions in London which charge, and you have listed 3 of them. Most museums and places of interest are free, and there are dozens upon dozens of them, from quirky to mainstream. Some have pretty good views too.
What I think you are doing unfortunately is - with the Tower of London, Westminster Abbey and Cabinet War Rooms all in one day - trying to fit a gallon measure into a pint pot.