BA has never been in favour of HAL's R3 proposal, at least publicly. The last thing WW wants to see is BA's profits being cannibalized by a combination of higher airport charges and increased competition at the main base. He's already got plenty of LHR slots thank you very much through his acquisitions of BMI and Aer Lingus.
Easyjet probably has similar concerns about the R2 proposals at LGW.