Of you list of sights, the British Museum and the National Gallery are free, so no reservations or tickets are needed.
For many of the others, buying in advance online not only avoids ticket buying lines/queues, but also saves £1-5 per ticket. For any place you're thinking of, look at their website now, and see if you can create an account. This will save time and make it easier to buy a ticket "on the fly."
For instance, when I went to Greenwich to see the Royal Observatory and Cutty Sark, on the morning I decided to go, I logged into my account and bought the ticket. I saved £5.25 on the ticket, and since I had already created the account, it was easy to buy the ticket on my phone. The website was not clear on whether I could scan the ticket from my phone or needed it printed. My hotel printed it for me, but it turns out the PDF could have been scanned off the phone.
Of the sights on your list, the Tower of London, Westminster Abbey, St. Paul’s, the Transport Museum, and the Cutty Sark all have discounts for advance booking. Again, for many of them, the morning of is far enough in "advance," but do check each website to be sure of the latest policies.