The servisair lounge in T3 is nothing special - afraid I can't remember if it has internet access. I suppose it comes down to how long you expect to be there. Bear in mind it might not be close to the gate you need to be at.

I think PP is expensive when bought as a standalone.... but can be worthwhile with Amex Plat. £300 a year including 2 PPs (version where all visits are free) and travel insurance for your supplementary/additional cardholders. Or Morgan Stanley's i24 card includes it for £275 a year - plus their credit card is % free on foreign currency transactions.

Sounds like for this trip it might not be worthwhile. On my last couple of trips through LHR, security has been so slow (even with fast track which I'm guessing you won't have this time) that I never made it to the lounge anyway.