Interesting stats....
1. Yes, the UK rollout is doing quite well. 55% adult population with 1+ doses per https://coronavirus.data.gov.uk/details/vaccinations
2. The US, despite its much-derided healthcare system, has hit 26% (all population) with 1+ doses per https://www.nytimes.com/interactive/2020/us/covid-19-vaccine-doses.html
3. The EU ... less than half the US performance it seems! https://www.ecdc.europa.eu/en/covid-19/vaccine-roll-out-overview

However we can still expect the UK to headline on no of deaths attributed to COVID, although the reporting data is less standardised for that! No 9 in world rankings / no 1 in major economies... https://edition.cnn.com/interactive/2020/health/coronavirus-maps-and-cases/

M3W5sp 2015, MSCC, MTWC, Oxon UK