Lord Robert Hayward - who has conducted detailed research into May’s elections alongside polling company ComRes - added that the party could also expect to lose support if Brexit remains unresolved.
Speaking at a briefing to journalists in central London yesterday, he said: “There is a Brexit benefit to the Government if there is a deal.”
And he added: “There is clearly a disadvantage, disbenefit, deficit to the Tory party of not having a deal.”
Although he also warned that the Conservatives looked set lose seats across the country whatever the state of the Brexit negotiations, which he suggested would result in a boost for the Liberal Democrats and to a lesser extent, Labour.
Lord Hayward said the prediction was based on feedback from voters which found that there are a “large number of people who just want it over with.”
The polling expert also forecast a low turnout as, he said, people of all political colours, had become “so hacked off with politics in general they just won’t vote”.
Meanwhile, it emerged that nearly 156,000 people have applied to register to vote in the past seven days - the highest weekly total so far this year.
A total of 155,592 applications were submitted in the week ending April 7, according to Government figures.
This was up 10 per cent on the previous week, and almost double the total at the start of the year.
The spike in applications ahead of the local elections may also reflect growing public expectation of other polls in the near future, such as European elections, a second EU referendum or even a general election.
More than half (51 per cent) of the applications submitted in the past week were from people aged 34 and under, while just 9 per cent came from those aged 65 and over. Local elections will take place on May 2 across most of England, with the registration deadline set for this Friday.
Seats on 248 local authorities will be up for grabs, including five newly-created councils: Bournemouth, Christchurch & Poole; Dorset; East Suffolk; West Suffolk; and Somerset West & Taunton.
In areas including City of York and Scarborough, all seats are up for grabs.
If the UK takes part in this year’s EU parliamentary elections, the deadline for people to apply to register to vote will be May 7.