The country faces a shortage of troops in the campaign against Russia's better equipped and larger military
The poll, by public opinion research firm Kantar, showed 22% of respondents said they would definitely or probably not get a coronavirus vaccine, rising to 38% of 18-24 year-olds.
Only 5% of those aged 65 and over and 16% of those aged 55-64 said they would probably or definitely not get vaccinated.
Kantar said the poll found that 75% of people with a degree-level of education planned to get the vaccine compared with 57% of people without one.
Health minister Matt Hancock said on Tuesday that vaccinations for COVID-19 will be optional in Britain.