There's a wealth of vaccination data breakdown to the nth degree here
COVID-19 vaccinations This section contains information on the total number of COVID-19 vaccinations provided by the NHS in England in the seasonal campaigns. This data is sourced from the Data Processing Service (DPS), and is classified as management information. Data Autumn/Winter 2024/25...
www.england.nhs.uk
The current overall UK adult vaccination percentage (1st doses) is reported as ~66%
Looking at the three Bolton constituencies they report from that link
| Pop 16+ | Vaccinated | % vaccinated |
Bolton North East | 86,481 | 46,844 | 54% |
Bolton South East | 92,666 | 45,777 | 49% |
Bolton West | 85,081 | 51,828 | 61% |
The data is a week old, but it looks like Bolton as a whole is a fair way behind the UK, and Bolton SE lagging the most. I don't know Bolton at all but I'm guessing Bolton West is the posh bit!