Morning trip in London - is this itinerary doable?

I'm arriving into London pretty soon at night - and will stay at a hotel near Euston station (where I'm planning to catch a train to my final destination near Birmingham at 1pm on a weekday). First time visiting the UK and was planning to look around London in the morning with the following itinerary - was wondering if this is doable.

  • 7:30-8:30 am - Euston hotel -> Walk to King's Cross/St. Pancras station and catch Circle line tube to Tower Hill, see Tower Bridge during sunrise

  • 8:30-9:30am - catch the ThamesClipper/Uber Boat ferry from London Bridge Pier nearby to reach Westminster. See Big Ben, Westminster Abbey

  • 9:30-10:00 - walk to Buckingham Palace

  • 10:00-10:45 - walk to Green Park station and take Bus 14/19 to reach the British Museum

  • 10:45-12:00 - have a quick look around British Museum. Looking to see only specific exhibits inside and I've already booked a ticket in advance around this time.

  • 12:00-1:00 - walk back to Euston hotel, check-out, reach Euston station in time for the train.