For same day confirmed travel (boarding card in possession then yes) use the app to generate your boarding card. They should place your purchase in a STEB bag with the receipt visible. No huge deal as you will be reclaiming baggage in LHR in any case. They may however be funny these days with landslide transfers, but in the past I have done it.

If you are denied the opportunity you can avail of world duty free in LGW N Terminal departures lounge. Better collection of shops than T3 MAN in any case. And all RRP prices based on London for all WDF stores, regardless of airport location.