The Bow Group, Britain's oldest conservative thinktank, says privatisation is so unpopular with voters as to risk damaging Tory vote in 2015

Rural Conservative MPs are worried that the Tory-led privatisation of Royal Mail is so unpopular with voters that it may cost them their seats at the next general election.

The Bow Group, a leading rightwing thinktank, claims dozens of Tory MPs have raised concerns with the party leadership that the £3bn privatisation of the 497-year-old postal service is "so unpopular it could risk their vote at the election".

Ben Harris-Quinney, chairman of the Bow Group, the oldest conservative thinktank in Britain, said: "Conservative MPs representing rural constituencies that don't have a particularly big majority are concerned. They are raising these concerns with us and the leadership."

High-profile Tory backbencher Nadine Dorries said she was totally opposed to the flotation.

"HS2 [the high speed rail link to the north] should have been scrapped and the money invested in Royal Mail – RM has turned around of late and is in profit. It needed more time, it's a great British institution – [with] postal workers amongst the best in the land. We will regret this and Labour's hypocrisy is staggering," she said.

Dorries said that any Tory MP in a marginal seat with a large number of postal workers in their constituency was likely to privately oppose the sale.

Tories who have publicly raised concerns include Brian Binley, the MP for Northampton South who sits on the business select committee, Daniel Kawczynski, the MP for Shrewsbury and Atcham who defied the Tory whip to vote against privatisation in 2009, and Sheryll Murray, the MP for South East Cornwall who is concerned about the effect the sell-off might have on rural services.

Harris-Quinney said rural Tory MPs were facing a difficult dilemma about whether or not to toe the party line as it was "pretty clear this privatisation is a very unpopular policy with their constituents".

He warned that the main groups of voters opposed to the privatisation – those living in rural areas and the over-40s – were "also those that have a strong tendency to vote Conservative".

He said: "If the Conservative party and the government do not [raise public awareness of the arguments for the sale] then I think there is a real risk it will damage the Conservative vote in the 2015 election."

He warned that privatisation could help Ukip take Tory votes. "People see Royal Mail as a part of the patriotic fabric of our country," he said.

"[The sale] shows the party is being operated by [the Tory leadership] in a bubble away from the Tory base and the voters.

"That has helped Ukip support. [Ukip leader] Nigel Farage has done very well out of this. He is seen as a bloke in the pub you can have a drink with – and he is."

Harris-Quinney said that, after approving same-sex marriage and the sale of Royal Mail, Tory voters were beginning to "feel the leadership of the party is running away with policy ideas not reflected by the base of the party".

He said the lack of public consultation over the sale "contributes to the perception that the leadership of the Conservative party is … not listening to what the public think".

Harris-Quinney said Michael Fallon, the business minister in charge of the sale, needed to do more. "Fallon thinks he's got out there as much as he can to promote the sale, but it has mostly been at political events. He has not been speaking to your average man on the street in Wolverhampton."

A YouGov poll commissioned by the Bow Group in July found that only 53% of people were aware of the privatisation plan and 67% of the public opposed the sale. A poll by Telegraph.co.uk found that 72% of 1,400 readers were against the sale.

Harris-Quinney said Tory voters were also concerned that the government may be selling Royal Mail off on the cheap. "There is a perception that [the sale] is to get the Treasury a short-term win but [the government] has not stopped to think about the effects for the economy in the long term.

"There is an argument that the assets [of Royal Mail] alone run into billions."