London Itinerary for upcoming 4-1/2 day Trip – what are we missing / how should we organize?

London Itinerary for Our 4.5-Day Trip – Seeking Your Thoughts!
I’ve posted a couple of questions here before and received fantastic help—thank you! I’m looking for any last-minute tips or feedback on our itinerary. Keeping it straightforward without a strict timetable; I hope it’s clear enough.
Thursday, March 27: Arriving at LHR at 8:30 AM, I expect we’ll reach our hotel near Trafalgar Square around 10:30 AM. We’ll grab lunch and freshen up before heading to Westminster Abbey for our 2:00 PM visit, which should wrap up around 4:30 PM. After that, we’ll return to the hotel to change for my son’s birthday dinner at 6:00 PM, then call it a night.
Friday, March 28: Planning to visit the Tower of London at 9:00 AM (our first entry time), followed by lunch and a stroll across Tower Bridge. We aim to head back to the British Museum for our 2:00 PM entry, likely finishing up around 4:30-5:00 PM. Open to any recommendations for that day!
Saturday, March 29: Our day starts at St. Paul’s Cathedral at 10:00 AM. We’re thinking of lunch and a walk to the Globe Theatre (not planning on seeing a show) and then crossing the Millennium Bridge. We’re flexible for the rest of the day, so suggestions are welcome!
Sunday and Monday, March 30 and 31: No specific plans in place yet.
Tuesday, April 1: We’ll head back to LHR for our flight to Chicago.
Things We Want to See: The Churchill War Rooms, Buckingham Palace (just a walk-by, no tour), Hampton Court, and the London Eye (a must-do for our kids).
We’ve intentionally kept our schedule open to allow for spontaneity and suggestions from this sub. Also, if you have any recommendations for dinner spots with allergy-friendly options, I’d appreciate it!
Thanks in advance! Wish us luck!
Your itinerary looks great and allows for a nice mix of sightseeing and flexibility! Here are some suggestions to help you optimize your time and include a few more activities:
Thursday, 27 Mar
Friday, 28 Mar
Saturday, 29 Mar
Sunday, 30 Mar
Monday, 31 Mar
General Tips
Have an amazing trip, and happy birthday to your son! Enjoy your time in London!