David Cameron is standing by Culture Secretary Jeremy Hunt despite continued Labour claims he misled Parliament and broke the ministerial code.

The Cabinet minister held onto his post after the Prime Minister decided not to order an investigation into his handling of the News Corporation bid for BSkyB.

A Downing Street spokesman said evidence given by Mr Hunt during a six-hour appearance at the Leveson Inquiry showed he "acted properly".

Mr Cameron's decision not to refer the matter to Sir Alex Allan, the Prime Minister's adviser on the ministerial code, was "disgraceful", Labour's deputy leader and shadow culture secretary Harriet Harman said.

The announcement that Mr Hunt would not face a further investigation came within minutes of the conclusion of his evidence, fuelling Labour claims that the issue was being "swept under the carpet".

Mr Hunt told the inquiry he considered quitting following the wave of allegations about his handling of the takeover bid. He said: "I did think about my own position. But I had conducted the bid scrupulously fairly throughout every stage and I believed it was possible to demonstrate that and I decided it wasn't appropriate for me to go."

Mr Hunt did accept, however, that chatty messages he exchanged with James Murdoch while he was responsible for deciding on the BSkyB issue were, with hindsight, inappropriate.

A Downing Street spokesman said: "Jeremy Hunt's evidence has shown that he acted properly while he was responsible for the BSkyB bid. He took independent advice at every turn, as well as a number of decisions which were against News Corporation's wishes."

But Ms Harman said Mr Hunt should never have been given the quasi-judicial role over the takeover "as he was biased in favour of the bid".

She said: "Jeremy Hunt should not be in his job now as he has broken the ministerial code and misled Parliament. At the very least, David Cameron should refer him to the independent adviser on ministerial interests. David Cameron said he would stand up for high standards but he is sweeping this matter under the carpet."