I am finalizing plans for our trip for myself and 2 friends in London for 2.5 days the first of Sept. We know we want to see St. Paul's Cathedral, Tower of London and Westminster Abbey, and I would like to see the Churchill War Rooms if there is time. Does buying tickets on line for those places before we leave save us time standing in lines? We don't want tours, just entrance tickets.
Thanks for any help!

Not really since even ticket holders have to go through security. The way to miss the long line at the Tower is to get there just before opening time.

The others don't have enormous lines.

Plus, if you want to use the 2for1Days Out discounts you cannot pre purchase tix.

We bought a combo ticket for the Tower of London and Tower Bridge experience over the Easter break and it did save us a good bit of time. Particularly for the Tower Bridge experience(not on your schedule) where there was a very long line to buy tickets and we sailed on past - we got to the top just as the bridge was opening to let a ship pass underneath and we would have missed that if we had to queue. There was a large but fast moving queue to buy tickets in the Tower of London tickets building (across the road from the entrance, you queue again at the entrance for security check) and we could just go straight to the entrance with our pre-printed tickets.

We couldn't buy the 2 for 1 discounts as they were not valid over the Easter holidays, so that wasn't a factor for us.

The only place we pre-purchased was for Windsor Castle - bought a voucher at Waterloo station with our train tickets (no 2for1 for crown properties) and skipped a LONG ticket-buyer line to get to the box office set aside for ticketholders.

No problems at the Abbey or Tower . . .

If you are using mass transit, an Oyster card loaded with money can speed up entry, bypassing ticket booths etc. The War Rooms are interesting and took me about an hour (although I knew a lot about the subject.) No line-up in mid-afternoon that day. If there is a long line-up, the inside is probably full of people making it harder to appreciate the displays (by necessity it's pretty cramped.)