David Cameron's most senior civil servant has rejected Labour calls for an inquiry into alleged breaches of the ministerial code by the Prime Minister as a result of his links to Conservative elections adviser Lynton Crosby.

Cabinet Secretary Sir Jeremy Heywood said that, as Mr Crosby was employed by the Conservative Party and does not "advise or lobby on Government business", he could see no purpose in an investigation.

In a letter to Labour leader Ed Miliband, Sir Jeremy revealed that the Australian lobbyist had agreed "principles of engagement" with the party when he took up his advisory role, pledging "not to use access to ministers or special advisers to influence or lobby for changes in Government policy on behalf of his firm's clients".

Mr Crosby, whose lobbying firm CTF Partners is reported to have worked for tobacco giant Philip Morris, denied he had had talks with Mr Cameron on the subject of plain packaging of cigarettes.

His denial follows a string of stories about whether his advice to Mr Cameron was influenced by his company's work for firms involved in the smoking and alcohol industry, private healthcare and shale gas "fracking".

Mr Miliband accused Mr Cameron of "bringing big tobacco to the heart of Downing Street" by hiring Mr Crosby shortly before shelving plans for standardised cigarette packages.

But in a statement issued yesterday by CTF Partners, Mr Crosby said: "The Prime Minister has repeatedly and clearly said that I have never lobbied him on anything, including on the issue of tobacco or plain packaging of cigarettes.

"What the PM said should be enough for any ordinary person but to avoid any doubt or speculation, let me be clear: at no time have I had any conversation or discussion with or lobbied the Prime Minister, or indeed the health secretary or the health minister, on plain packaging or tobacco issues.

"Indeed, any claim I have sought to improperly use my position as part-time campaign adviser to the Conservative Party is simply false."