I live in London
There's much more to see at Westminster abbey if you're picking a church and the audio commentary is really good - this is worth paying for as an attraction
St Paul's - go to the service and you don't pay - 5pm is usually evening service and you wander around before and after. I went to the communion service a few weeks ago and it was really moving to see so many nationalities taking communion together. Plus the servers/the priest/ all women service
Kew is amazing but is definitely a whole day
Get the Uber boat up and down the river (you just tap in and out with your debit card). Do not pay to go on a tourist boat. That way you can go to Tate modern, jump on the boat and go to Tate Britain
There are some glaring omissions from your itinery - the National portrait gallery was reopened by Princess of wales last year and it's amazing - I would go that over Tate Britain. Cafe very good but st martins in the fields church over the road has an underground crypt cafe which has home made soups/nice mains etc - bit cheaper
Tate modern is great if you haven't seen it
The same Uber boat to Greenwich in the other direction is the other omission- the royal observatory, walking round the royal naval college, the queens house, the National maritime museum, the painted hall - I live 5 minutes walk
away so im biased and thinks it's unmissable
plus you can then see all the bits where the latest Bridgerton plus poldark was filmed. Greenwich is a full day out, opposite on the Isle of Dogs is the (free) museum of London docklands - again you just get the boat over (or walk through the foot tunnel)
John soane and denis severs are both incredible (you don't need the hunterian on top of that) - you need to book severs in advance- it was really hard for me to get tickets a few years ago and I had to wait weeks for a slot
If you love dickens the (paid) dickens museum in Bloomsbury is great.
I'm sure you've missed out the British museum/the V and A/the natural history museum because they're all massive and take pretty much a day each !
Download the today tix app and see a show for £15/£20 - I see dozens of shows a year (it's my thing) - and this is pretty much the cheapest way to do it ad hoc