London 48 hours next week 6/23-6/21 Itinerary Sanity Assist..?

Am confused about having tickets for the British Museum, is this for a particular exhibition?

Think you are trying to cram in way too much, and on arrival day some/all of you may have serious jet lag.

The Thames boat tour is the thing I've liked least during my numerous trips to London. I wouldn't waste my time. Maybe get the brass rubbing out of their systems on that first day or do the Tower that day. I think Tower, British Museum, and Westminster on same day would be mentally exhausting.

Try and keep everyone outside in the fresh air as much as possible. That will help to handle the jet lag easier. Try and avoid anything involving lengthy periods of sitting down, a recipe for nodding off which won't help.

To try and do the British Museum, Tower and Abbey in one day isn't realistic - especially when you suggest you would spend 3 hours at the Museum. That would suggest to me that you would spend similar times at the other two. That makes 9 hours without travelling or lunch. That makes for an 11 hour day.

For your boat ride, just use a standard commuter boat - probably from Bankside given your plans. A fraction of the price for a single - but even rover tickets would be way lower (£21.20 adult, £10.60 child, £42.40 for a family rover that would cover two adults and three children, as the 17yo would count as an adult)

Firstly on 25 June I didn't think there were any trains running from KX to York- as far as I know that is St Pancras to Bedford, rail replacement coach Bedford to St Neots and train St Neots to York.

As you are staying at the Tate Modern the water bus service you want (from Bankside Pier) is Thames Clippers. As you will see services run far into the night and you can get day rover tickets.
Although most seating is inside there is an open back deck which you can use for fresh air.

Although you have a timed entrance for the British Museum that wasn't really necessary, and you can turn up earlier if you want. Likewise the Tower of London you no longer need to book a time slot- you can turn up. Likewise Westminster Abbey you should be able to just turn up, especially in the afternoon.
The normal London Bus Route #15 between Tower Hill and Trafalgar Square is a good sightseeing bus route. From Trafalgar Square it is a very short walk down to Embankment Pier for the waterbus.
On the Saturday evening there is an evening concert at St Martins in the Field so you could visit there late afternoon, have supper and then go to the 1 hour Concert.
I think you will have to choose between Westminster Abbey and the Tower of London.

Thank you all for your insight and information.

The experienced grandson tells me he didn't enjoy the Westminster visit as much as his mom and I did, so I think I yield that since British Museum and the Tower appeal to both boys. Water buses instead of Thames tour suit our style - I think we went to Greenwich via boat and back atop a bus to our hotel near Victoria station.

Saturday evening meal at St Martins with a concert for me and brass rubbing for them is just the thing.

I'm now a little freaked out about a Sunday train to York - a daughter assured me there'd be trains....

Normally your daughter would be right about the train to York.
However there is rail engineering work going on.
You need to go to the LNER website and book a ticket. That will give you your timings.
There will be lots of staff around at Bedford and St Neots to guide you so it is an inconvenience, but not something to worry about.
The train from St Pancras to Bedford is a Thameslink train so has plenty of capacity.
Note that there are no advance fares available for that day due to the coach replacement.
So you will pay £68.40 each for the adults, which is a Super Off Peak Single. That has the advantage of being available on any train which further reduces the stress.
Looking at your previous post, I hope you bought a family and friends railcard as that will save you £61.15 just on this journey.

There is an alternative train option on the day, although not necessarily better. You can get a train from St Pancras to Derby and then change to York. So that's only one change and no bus ride, but irritatingly there is a one hour wait at Derby. So it will take 4.25 hours rather than 4 via Bedford and St Neots.