The phenomenon was first identified among the over-65s, but now includes those 10 years younger who have also started to receive their Covid jabs, they said.
Millions of voters will to go to the polls in local and mayoral races in England, as well as elections to the Scottish and Welsh parliaments.
For many, the May elections will be the first opportunity to cast a ballot since the 2019 general election, which saw Boris Johnson swept back into Downing Street on a wave of support from ex-Labour “red wall” seats.
Since then, Labour and the Liberal Democrats, as well as Scottish Labour and the Scottish Conservatives, have elected new leaders who will hope to make their electoral mark.
But the success and timing of the government’s vaccine rollout could pose significant problems for the opposition parties.
The local elections have often proven difficult for the ruling party, as governments tend to lose council seats and opposition parties tend to win them.
But Lord Hayward said: “It is the older generations who have moved most markedly to the Conservatives. Now the significant thing is, they are the people who vote in local elections.
“It is quite noticeable. It was, first of all, the age group from 64 upwards that moved. There’s some sign now that the 55-year-olds and upwards are also moving. And interestingly enough, they are the people who have received their vaccinations. So there’s clearly an element of vaccine bounce. I think it goes hand in hand – I don’t think it’s chance.”
The boost in support offers opportunities and risks for the Tories, however.
If people start to return to normal life after being vaccinated, their minds could turn away from Covid and towards other, more traditional political issues.
Voters go to the polls on Thursday 6 May.
Almost all areas in in England are expected to start counting votes the following day.
Because a number of elections will be held at the same time in some regions, counts could last well into the weekend.
The Conservatives could also face a nervous wait for the outcome in Scotland.
The Scottish National Party has said that a victory in the Holyrood elections would be a mandate for another independence referendum, a vote which could dominate much of the rest of Mr Johnson’s premiership.
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