You'll have to go through immigration anyway (not that it's a big deal if on an EU passport) even if the transit route is open - I believe that just skips customs doesn't it?

The only exception to this is if arriving and departing at the "A" gates (whatever they're called now) where arriving and departing passengers mix at the gate .. but BA never use them and I don't think EI LHR arrivals would either

Certainly do-able on the same plane - if you're sitting up front you'll be landside within well under 5 mins .. then just go straight back upstairs and into the security queue to go landside - apart from early and mid morning theses queues are never that bad in my experience and are usually well enough organised - at worst you should be able to get from the aircraft door back to the boarding gate in 20 mins, probably less than this.

I'd be slightly wary of going from an EI arrival to a BA departure as you don't then have the "comfort" that if your arrival is late so will your departure as its the same aircraft.