I wasn't in on Thames last week - so cannot actually comment on your situation but as others have said, it is unlikely that any action has been taken if you have heard nothing.
We get traffic at 2800 all the time under the TMA around Biggin (one today 15 E of LCY at 3200)
Now, if you were at 2650 under the ILS for 28 at LCY and the inbound over the top was at 3000feet and took a TCAS climb paperwork would have to be filed and you would probably have been closely followed back to your unit for identification.
As long as you have learnt from it. And if you don't have your Mode C on, other traffic with TCAS outside CAS (Posh helis/bizjets etc) won't get any TCAS avoiding action on you - so leave it on I would suggest.
Oh - and the London QNH is entered into the Radar equipment and shows on our screens - meaning that the Mode C we see is adjusted accordingly from what has been received by the radar.