Have you checked other UK airports, Manchester for example? We priced flights to the USA from London to be around £700, from Manchester to the same destination, same airline, it was £640, the irony being that we would have flown Man-LHR then joined the same flight for which they wanted £700, to do with airport charges, LHR is always expensive.
How much is BA to Amsterdam? If you're booked on the same carrier, or code share carrier, then your bags can be checked right through.