The £80 UK departure tax for longhaul premium classes is, as its name indicates, for departures out of the UK, not for connecting in the UK.

Quite often airlines erroneously charge the tax for connecting flights, but it's definitely not chargeable for international to international connections in the UK, see section 4 in http://customs.hmrc.gov.uk/channelsP...00505#P34_2871.

If I understand correctly, the OP is being quoted this tax for a XXX-LHR-YYY itinerary, where XXX and YYY are not in the UK. If that's indeed the case, it is a mistake and the OP should ask for the tax to be recalculated.