The two problems are: 1. the day to go to the Tower of London and; 2. the use of a bus in London.
When we signed up for the Best of England tour, Westminster Abbey (WA) was scheduled for Day 12 (the day you arrive in London from York) and the Tower of London (ToL) was scheduled for Day 13 (the full day in London) . Some time later the itineraries for these two days were switched. A big mistake. Rick's advice in all of his tour books and his shows is to get to the ToL early to beat the crowds and go see the Crown Jewels first before a long line builds up. Because of the switch in itinerary (and the use of a bus, see 2 below) we did not get to the ToL until mid day. The crowds were awful and, with the limited time we had, we had to choose to take either the Beef Eater Tour or to see the Crown Jewels. No way could you do both. If, as originally scheduled, we had gone on Day 13 we would have arrived when the ToL opened. We also would have had a lot more time at the ToL which was greatly needed.
Okay, who in their right mind uses a bus to go cross town in London when there is a direct Tube to where you are going. On arrival at London Paddington Station from York a bus met us and took us to the ToL. We spent at least an hour in the London traffic. There is a direct Tube line from Paddington to the Tower Station. So much quicker. Then again on the way from the end of Thames River Cruise we took the bus to our hotel and lost another 1/2 hour in traffic. Guess what, there is a Tube line from Westminster, where the pier is, to the hotel we were staying at. What about luggage? Hire a lorry to meet us at Paddington and take the luggage to the hotel. I expect that a short time use of a lorry would cost a small fraction of the cost of the bus for a full day. Oh, Oyster Cards for the Tube were already purchased for every one in the group so this would not be an additional expense. The tour group using the Tube would have been no problem as we did it the next day to go to St Paul's Cathedral (WA was closed to the public that morning because of a special service). All this wasted time meant we did not get to our hotel until 6:00 PM. This is the day the itinerary says "Tonight is a perfect evening for the theater (book something in advance online or pick up a ticket in London)". Luckily we had advance tickets and had just enough time to get to the theater. There was no time for dinner. Again, luckily we had not booked a show and dinner package. Those who did not have advance tickets had no chance to pick up a ticket in London.