Don't you get the P45 after you left your old company? Which means they can only look at it after you were hired.
Also, why is it the employee's responsibility to not drive inflation? If the company is fine with paying someone X for a job, why does it matter what the person earned before?
Well, that would be a great first impression if the very first thing the company found out about you was that you've lied in the interview about how much you've earned before.
