From what I understand having checked about UK citizens flying into the USA some weeks ago as I was supposed to go for a work trip in May....
If you have an existing ESTA and try to fly to the USA, your ESTA will be cancelled and next time, you will have to apply from scratch. You won't even be allowed to check in, let alone board.
If you have a valid ESTA, don't attempt to fly to the USA, and its expiry date will be preserved.
Somehow the BA check in system is linked to valid ESTAs - possibly it is the same with all airlines.
My ESTA expired shortly after I was due to fly to the USA but at the moment you cannot apply for an ESTA.
There may still be passenger planes flying from the UK to the USA, but most are full of cargo where the seats would normally be, the seats having been removed.
Safety first, and at the moment that means stay at home, no matter how important to you the reason may be to want to vist the USA.
Take care