On the higher population density, it's worth saying that I watched the spread of the delta variant work its way London-wards from north Kent (Swale, that's around the Isle of Sheppey). That's not an area recognised for high population density but that's where it prospered and spread from. The arrival of delta as the prevalent strain in London did not make for worse figures than it did for the rest of the country. And, curiously, the only places where infection rates show as below 200 in 100,000 on this current BBC link to government data
https://www.bbc.co.uk/news/uk-51768274 - are 9 inner London boroughs, plus Shetland and the outer Hebrides. Sparsity of population off mainland Scotland, sure, but definitely not in inner London.