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There are some truly excellent BA First Class fares available at the moment to the USA, as long as you are prepared to start your journey in Oslo/Prague/Budapest/etc.
German blog YHBU has a list of the prices from the various European cities you could fly from, but I’m just going to focus on the very best deals here, which seem to be from Oslo:
Oslo to New York (via London Heathrow): £1,878 Return
Availability is wide open and easy to find using Google Flights.
Oslo to Los Angeles (via London Heathrow): £1,900
There are plenty of other options too, like San Francisco, Phoenix, Dallas, Las Vegas, Seattle, etc for £100-£200 more.
I would suggest that a better idea though, would be to credit the flights to Alaska Mileage Plan instead, where you would earn ~52,000 (very valuable!) Miles. I would personally value 52,000 Alaska Miles at about £950, so you’re looking at getting half the cost of your ticket back in Miles! If you’re wondering why I rate Alaska Mile so highly, have a look at some of the incredible ways you can redeem them here.
You would also earn ~28,000 Elite Qualifying (status) Miles, which would get you MVP status, over half way to MVP Gold, and nearly a third of the way towards MVP Gold 75K:
If you fancy giving American Airlines First Class a spin instead, you can find fantastic fares to Miami:
Oslo to Miami (via London Heathrow): £ 1,749
Note that you’ll earn fewer Miles crediting AA flights to Alaska than crediting BA flights though (about half as many as on a BA flight of the same length).
First Class for the price of Business Class – and earn A LOT of Miles at the same time. Still expensive, of course, but not completely stratospheric.