David Cameron conceded today that his Government must "raise our game" as he sought to fight back after a "difficult" month of intense criticism of key policies and its handling of a series of controversial situations.

The Prime Minister insisted his "driving vision" remained intact and defended his own performance in Number 10, though he said ministers had to "learn lessons" about communicating with the public.

His administration has faced a sustained barrage of attacks over controversial tax measures in the Budget and handling of issues such as the planned strike by fuel tanker drivers and the attempt to deport radical cleric Abu Qatada.

The highly-trumpeted re-arrest of Qatada ended in farce amid a dispute between the Home Office and the European Court of Human Rights over exactly when a month-long window for an appeal had closed.

Mr Cameron defended under-fire Home Secretary Theresa May over the case, telling the BBC Radio 4 Today programme that the Home Office had "checked repeatedly" with the court during the process.

"It had checked repeatedly throughout that process, it was working on that basis and all the case law pointed in that direction so it was very clear and Theresa May has been very clear about this," he said.

"The Home Office was working on the basis of the deadline being the Monday night and that is something that they had checked with the court."

He went on: "They were told throughout that the deadline expired on the Monday night.

"Was the Government right to try to move as rapidly as possible to remove this man from our country because he has no right to be here and is a threat to our country? I think they were."

Asked about the tough time faced by the Tory-led coalition with the Liberal Democrats, he said: "Everything we are doing is about helping people who work hard and do the right thing and making this country more pro-enterprise, more pro-get-up-and-go, more pro-work, more pro-effort.

"That is the driving vision. That is the mission.

"You have difficult weeks or difficult months. I want us to raise our game and do better. But the vision and the long-term are what matters."

He went on: "In two years, to have a couple of bad months is not surprising."

Responding to claims that he was not giving the job his full attention, he said he was working "very, very hard" but that it was vital to maintain family life to avoid becoming "fried and exhausted" and make mistakes.

"It certainly doesn't feel like that from my perspective. It is a huge honour to do this job, it is an immense privilege. It is extremely hard work, I work very, very hard at it. I am normally at my kitchen table at quarter to six in the morning going through my boxes and papers.

"I try to have around me a very strong team of people and I am fortunate in an excellent Cabinet."

But he acknowledged that mistakes were made over the potential fuel strike - notably Cabinet Office Minister Francis Maude's call for voters to fill "jerry cans" with petrol and keep them in their garages.

"I accept we need to learn lessons around communication," he said.

Responding to criticism that he was seen to devote too much time to the school run, "date nights" with wife Samantha and watching DVD box sets, he said: "It has got to be possible to be a decent husband, a good father and a good Prime Minister at the same time. If it isn't possible then there's something wrong."

Voters accepted that their leaders would not get every call right, he suggested.

"What they want to know is that your average does not fall too low. But if you are completely fried and exhausted and have no time for your family and never go for a jog or play a game of tennis or whatever, you will get into a situation where you will make very bad judgments."

Mr Cameron agreed it would be "sensible" for him to avoid involvement with individuals guilty of the kind of "aggressive" tax avoidance described by Chancellor George Osborne in the Budget as morally repugnant.

Asked if he would make sure in future that he had no dealing as premier with anyone in that category, he said: "Generally speaking, yes, I think that's sensible."

He had been pressed to comment on the tax affairs of retail tycoon Sir Philip Green, whom he recruited to lead a review of government costs.

"I am not getting into an individual's tax affairs on air. I would have to go away and look exactly at what they do," he said.

"I asked Philip Green to do a particular bit of work about cutting the cost of government. He came up with very sensible suggestions for how you could reduce costs in government and therefore reduce people's tax liabilities."

Mr Cameron said he still held by the pre-election slogan that "we are all in it together" despite claims the Budget - which saw the top rate of income tax rate cut from 50p to 45p - favoured top earners.

"We have had to take very difficult economic decisions but I do believe that we are all in it together and I do believe the Government is acting fairly," he said.

"For instance, the richest 10% are paying 10 times more towards dealing with the deficit than the poorest 10%."