If you are on the JFK-LGW service ( BA 2272 ), you would need to wait until the delay has been announced for that sector.
As you have mentioned, the incoming aircraft LGW-JFK ( BA 2273 ) is already delayed by 2 hours but unless you have Gold or higher status and get connected to a willing agent, I doubt that somebody would rebook you at this stage since your original flight has been delayed.

This is a very minor possibility but BA could also make operational decisions such as switching aircraft at JFK and another aircraft that comes from Heathrow operating your flight so keep an eye on thee Flight Status and once you would officially misconnect, call BA and ask for a rebooking.


Please ignore as BA 2272 was delayed from 20:10 till 22:10 while I was typing.
OP call BA and ask your options.