I'd suspect the answer you need for this is should be in your Ops manual under Fuel Policy or similar..
FWIW using our (EASA) ruleset for a day with no weather complications as long as you can land at the destination (LHR) with >= 30 minutes fuel, having held for the advertised time, then you can dispense with the Alternate (in this case LGW )...and continue holding for LHR..... There's no need to tell ATC of the fact ( TBH I suspect on a routine day if you told LHR director you were nominating the other runway as an alternate you might get a "err Roger" or a
.).
I'll emphasise that's the back of envelope answer and doesn't apply in all circumstances.