Working on London Schedule

The Abbey only opens at 9.30am on a weekday, 9 am opening only happens on a Saturday.
The walk to Buckingham Palace is about 15 minutes.
If you are up so early there are said services at the Abbey at 7.30am and 8am. While you can't exact!y dawdle before or after the services you get to appreciate the Abbey when empty as you walk through to whichever chapel is being used that morning.
Having said all that you are there at the end of Holy Week, just before Easter Day on 20 April. Especially on Friday 18 April visiting hours may be heavily constrained to allow for extra Good Friday services.
The train from Waterloo is the usual route to Hampton Court.

I went to London last year. I think the first morning’s activities are doable. However, I think the time at the Tower is a bit rushed. It’s a big place and usually crowded. I didn’t walk across the Tower bridge, so maybe others can comment if it’s enough time to get to the Globe.
Regarding Hampton Court, there’s a train that leaves Waterloo Station that takes about half an hour to get there. It was about £16 round trip during off-peak hours. Hampton Court was one of the highlights of my trip, enjoy!

I really like the verger's tour at Westminster Abbey and I think you may have given yourself too little time there if you want to take a tour.

Also, a taxi to Hampton Court from central London will cost you anything from £70-£100 or more if the traffic is bad, and that would mean it would take a lot longer too. Train is a much better way of getting there and the station at HC is just across the river from the Palace.

another vote for the train to Hampton Court Palace, and that includes a nice and very short walk over the River Thames when you get off the train.

I think that you are cutting the Tower of London very short.

(I'm a member at both and even for a member who visits both regularly I would normally spend more time at the Tower)

If you start to walk over to Buckingham Palace at 10:30 you will be at the back of the crowd for seeing the Changing of the Guard. Are you exceptionally tall? That might help.

Looks like that Friday is Good Friday and Westminster may not be available, so we will move to Thursday when we come in.

I do think we may need a little longer at Tower, so we will likely need to sacrifice a tour at The Globe, because it looks like they are only available 10-2...lol

Thanks for input all

Thursday of Holy Week is Maundy Thursday, so while the Abbey will be open for tourism, there are likely to be restrictions on times - perhaps check closer to the date. I suspect it will close quite early, and yes on Good Friday it's closed to tourists.

It will depend on your level of interest but the Tower of London has enough to keep you busy for a big chunk of the day. We spent 5 hours there.

The train to Hampton Court is easy and likely faster than a taxi. We also spent 5-6 hours there.

Last September my husband and I did something similar to your Tower of London day. We arrived at the Tower at 9 and stayed until about 12 or 12:30, including lunch in the restaurant. We then walked over the Tower Bridge and meandered along the Thames to the Globe. We arrived around 1:30 for a 2 pm performance (Comedy of Errors). I'm guessing we walked about 1.5 miles from Tower to Globe, stopping now and then. The views of the Tower and bridge are spectacular from this vantage point and we stopped often just to admire them. I don't think you would have time for such a leisurely walk, but of course there are faster modes of transportation like an Uber boat.

If you go to Hampton Court in an afternoon the train fare is only £10 return, £16 is only for weekday travel before 0930. As Good Friday is a public holiday the £10 fare applies all day, likewise on the Saturday and Sunday.

You could also do the return journey from HC (in whole or in part) by boat- https://www.thamesriverboats.co.uk/

The Ceremony of the Maundy Money seems to be at Norwich Cathedral this year, but in a year when it was at the Abbey (every 10 to 15 years nowadays) the Abbey would also be closed on the Thursday.

On Sunday, Easter Day, all big shops (food and otherwise) are closed by law. But convenience shops and tourist shops will be open