After the Tories' humiliating defeat in the Romsey byelection, Sir Malcolm called on Mr Hague to follow the example of Tories in Scotland, who are reaching out to new voters.
Ceri Evans, campaign manager for Steve Norris's run for London mayor, said Central Office should take a leaf out of Mr Norris's book and appeal to middle of the road voters who believed in "principled pragmatism". Mr Hague should resist calls from shadow ministers who wanted to exploit race as a campaigning issue.
There were signs yesterday that Mr Hague is heeding the calls of moderate Tories. He confirmed that he would be offering Mr Norris a job in Central Office, expected to be a vice-chairmanship with a special communications role.
However, the appointment is likely to cause tension among shadow ministers. One was dismissive of Mr Norris's mayoral campaign, saying that he had been out-polled by the party's assembly candidates.
The task facing the Tories, who are privately devastated by the Romsey loss, was underlined yesterday by Sir Malcolm, who said Mr Hague "had a mountain to climb". Moderate Tories were alarmed by Mr Hague appearing to pander to core Tory voters when he pledged to detain asylum seekers and spoke out for the jailed Norfolk farmer Tony Martin.
Sir Malcolm pointed to the Tory leader in Scotland, David McLetchie, who is wooing Liberal Democrat and Scottish National Party voters.
"To win their support will require hard effort, attractive policies and a moderate rhetoric," Sir Malcolm, president of the Scottish Conservatives, said in a speech at Bridge of Allan, Stirlingshire. Tories were "showing themselves to have such qualities at Holyrood".
The Norris camp said his mayoral campaign should form the model for the Tories' general election campaign. Mr Evans said Mr Norris had succeeded by "maximising the non-core vote with the minimum damage to the core vote".
"Steve's strength is that he is a dyed in the wool Thatcherite free marketeer who believes in a tolerant, inclusive society," Mr Evans said, views that "do not need to be mutually exclusive".
The Tory leadership insisted last night that Mr Hague had not lurched to the right and that he was addressing issues that concern all voters. In the coming weeks, he will speak on health, education and the environment to show that he is not a single issue politician.
Mr Hague said on BBC1's Breakfast with Frost that the Tories' success in the local elections, when they picked up seats in areas such as Wigan, Greater Manchester, showed that the party was reaching out beyond its core voters.
