As others have said, the taxes are only assessed on flights departing the UK (and, even then, are waived if you originate somewhere else and spend less than 24 hours on the ground in the UK on the same ticket).

In addition to that, the UK charges the same exact "sin tax" on premium economy tickets that they do on business class; if you're using miles or certificates to upgrade from PE to Upper Class, no additional taxes would be required because you already paid them as part of your base ticket.