I'm not sure that you will get access, as the rules are

Arrivals lounges are available at London Heathrow Terminal 5 and London Gatwick (situated in the Sofitel Arora Hotel) for:

First and Club World customers.
Gold Executive Club members who have arrived on a British Airways longhaul flight. Due to capacity restrictions, guests will not be permitted to use these lounges.


At that point you'd be a CE customer, rather than a CW one.