London has more young people and less old people than most of the country so it can reach a lot of the vulnerable while still vaccinating less than the rest of the country.
Once the vaccine refusers see the vaccinated have not grown a tail/starting buying Microsoft products/whatever else their tiny brains imagine take up of vaccines may increase even further. Plus some studies count as vaccine refusers people who are not able to have the vaccine currently or are pregnant and may prefer it later.
More of my older relatives have slots booked for vaccination, including the biggest doom merchant who kept insisting it would be March at the earliest and is booked in next week.