How does VAT refund work for visitors in London?

This should answer most, if not all of your questions: https://www.gov.uk/tax-on-shopping/taxfree-shopping

England doesn't participate anymore.

Yes indeed- the tourist VAT refund scheme was abolished in 2020.

And if you are on a multi-country tour be sure to pay attention. I have seen several people at Heathrow who were upset that they could not process VAT for purchases in the EU because they don't do that in the UK since Brexit. If you are doing the UK as your last stop do the VAT before you get there!.

Tax-free shopping
You can only buy tax-free goods from shops:
in Great Britain (England, Wales and Scotland) if they’re delivered straight to an address outside the UK
in Northern Ireland if they’re delivered straight to an address outside the UK and the EU

From the link Mardee posted

I have purchased a couple of items over the past few years that were shipped to the US. The VAT was removed.

Likewise I have found that ordering online ends up being cheaper- even when shipping is taken into account. For suits in particular I will try on in store and then order online, and I quite often buy things from Selfridges online as well. I love bookshops and usually can't resist when I'm in the UK, but do a lot of my shopping with Blackwells or Hatchards online, as well, and save on VAT.

The big exception is sales, which tend to be better than available online, even including VAT.

There's no VAT on books, however or wherever you buy them.

And that is something I did not know... thanks for sharing.