Yes and no - London much less vaccinated than the rest of the country
Perhaps a little less vaccinated, the non NIMS based data doesn't show such an extreme fall, it is also more prior infection than much of the country which almost certainly is more protective (even with maybe 10% of the cases being re-infections, that's still much higher effectiveness than the vaccine efficacy)
Also, it may well be slower, remember the first three weeks of Omicron spread in London there were no omicron specific mitigations, if the scientists have produced any mitigations that matter then they should slow it by the amount they claim - have they claimed any range of slowing from the new mitigations (vaccine passports etc.) ?