LayToLay
TCAS RAs in general are inhibited below ~1000R (the actual ruleset is quite complex), and become TAs.
Our QRH says to "respect GWPS warnings" during a TCAS RA, which to me seems sensible
That said, ~4000' over London in a widebody jet, low speed, half configured, I think it would be hard work to make oneself stuff the nose down to >2500'/m, almost certainly (but correctly) overspeeding the flaps in the process
which will now set off various loud bells to add to the TCAS / ATC / Crew Comms / maybe GPWS symphony
NoD