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You can currently book some superb BA First Class fares on direct flights from London to the USA, including San Francisco for £1752 return:
and New York for as little as £1,636:
What is absolutely fantastic about these fares is that you can book dates (from October) all the way through to the end of the current window in mid March 2022!
To quickly see a wide range of dates, I normally use Google Flights.
As is often the case, the very cheapest fares are via online travel agencies, which you can find on sites like Momondo here.
However, in the current travel climate, I would personally be tempted to pay a little more and just book direct with BA instead:
These are superb fares for direct First Class flights from London – particularly to San Francisco.