I've done it before but from the 1 to the 3.
Was on cheapo ex-dub £900 ticket. Asked at the ticking desk at DUB and said I needed to see family in London, two minutes later I had a boarding pass for BA3 instead of BA1.
I don't think they'd do it for you at LHR/LCY/LGW for free but they don't give a toss about the rules in the EU outstations.