If you pay for your ticket before 1st of Feb but travel after 1st Feb, they WILL make you pay the extra tax.
I remember flying on the day that Airport Passenger Duty was introduced and the airline had staff going up and down the check-in queue collecting the tax.
The American passengers near me were just dumb-struck that government would do this, but as usual the Brits there just got on with it and paid up without much complaint. As Pink Floyd so eloquently said "hanging on in quiet desperation is the English way"
Not for me. I jumped ship.