That's incorrect, the lockdown in November was not due to London. It was a response to a steep upward curve mainly in the Midlands and North East, but rises were starting to be seen everywhere when the decision was made except for one region in England (North West). Lockdown was announced on 31st October and put in place on 5th November, and peaks of 7 day average case rates were seen after the restrictions came in in the majority of areas according to the government dashboard:
North East: 10th November
London: 11th November
East Midlands: 9th November
East of England: 9th November
South East: 11th November
South West: 11th November
West Midlands: 11th November
London was actually on a far less steeper curve than the majority of other regions. At the time, the Midlands, especially West Midlands and the North East was of particular concern, but most areas were seeing a rise nonetheless. In fact, the regions who appear to have lost out if you solely look at cases were:
Yorkshire and Humber: 6th November
North West: 19th October
Yorkshire and the North West was likely due to the harsher tiers being in place in a lot of areas within those regions, hence the earlier peak. The Tees Valley area of the north east for example (that's me) was under Tier 2 pre lockdown. But then hospitalisation and patients on ventilation data will also have had to have been factored into the decision as well. I'd also speculate that schools returning from October half term also contributed to increases in cases too.
I can't find anything to argue against the fact that the national lockdown did have an effect on case numbers, when the data points to drops being seen when it was implemented in most areas. Even where data only shows things levelling off, without them an increase would likely be seen despite those tougher restrictions being in place.
My argument has always been what happened after lockdown ended on the 2nd December. Cases in London showed a shallower decline during lockdown compared to other regions, and the 7 day average began flattening off around the 20th November, before the new tiers were announced on the 26th November. Alarm bells then should've been sounding soon after the 23rd when that average started to increase even with the lockdown still in place.
The government had between the announcement on 26th November and when lockdown ended on the 2nd December to backtrack with an explanation to the public as to why London's tier should be revised, but chose not to. That's despite the 7 day average of London cases increasing between 26th November and 2nd December by nearly 10%, and from the start of the lockdown until the 2nd December by 17%. Politics took preference over health, and unfortunately we're all now paying the price for it.