For a little over £50 I'd go for the First Class ticket even if there's a risk BA might only pay standard.

Better seats, complimentary snacks and drinks, free (but usually slow) wifi, lounge access at kings cross. It's worth it for a journey that length.

Just send your receipt in for the rail travel, if they then reply they'll only refund standard say that the standard ticket is £152 and you're happy to cover the difference yourself.