Gordon Brown brushed off the threat of a leadership challenge after the disastrous defeat of Labour in the Glasgow East by-election.

The Prime Minister insisted he was simply “getting on with the job” after seeing Labour’s third safest seat in Scotland fall to the Scottish National Party with a massive 22 per cent swing.

He said during his visit to the West Midlands: “My full focus is on taking people through these difficult times.”

Mr Brown insisted that the Government was addressing public concerns about rising fuel and food prices.

“I know that people look to the Government to take the action that is necessary,” he said. “We are looking at everything we can so that, in what is a global problem, we can in Britain help people through these difficult times."

Conservative leader David Cameron said it was time for Mr Brown to call a general election.

Speaking outside his home in west London, the Tory leader said: “I think the Prime Minister should have his holiday but then I think we need an election.

“I think we need change in this country, and that’s how change should come about.”

Mr Cameron said he was pleased the Conservative candidate, Davena Rankin, went from fourth place to third place and “maintained” the party’s share of the vote.

“But what I wonder is whether we can put up with this for another 18 months,” he said. “I think whenever people have had a chance to speak about this Government, whether at the local elections, whether in Crewe, whether in Henley, whether in the London mayor elections and now in Glasgow, they have said ‘Look, we think you’re failing and we want change’.

“I think it’s the Conservative Party over the last few months that’s really been setting the agenda on things like how we combat knife crime, how we deal with the cost of living, how we clean up politics.

“And so I look forward to going on and setting that agenda and fighting that election whenever the Prime Minister calls it.”

However, Mr Brown brushed aside the call for a general election.

“I think my task is to get on with the job of taking us through these difficult economic times,” he said.

He was equally dismissive of the prospect of a leadership challenge, saying: “I’m getting on with the job”.

Mr Brown praised Margaret Curran, the defeated Labour candidate in Glasgow East, saying that she had fought an “excellent” campaign.

He stressed that with oil prices having trebled over the last two years and food shortages pushing up prices, every country in the world was affected by the current economic difficulties.

“Coming from ordinary families as we do and have done, we know what it is like when people go to the supermarket and find that the price of milk, and the price of bread, and the price of eggs have gone up dramatically in recent months,” he said.

“We know that our role when facing global economic challenges is to be on the side of hard-working families, on the side of the people of Britain.”

The Prime Minister added that if the Tories were elected they would push through a £12 billion tax cut paid for by cuts to health, education and other frontline services.

“I don’t want to wake up and find that there are massive tax cuts being given to the fewest and the richest and the wealthiest people of this country at the expense of cutting the public services of this country,” he said.

He ended with a rallying call to activists to have confidence in the party’s values, “whatever the setbacks and difficulties” that lay ahead.

“Whatever these difficulties, have confidence that not only do we have the right the policies, but when the time comes we will be able to persuade the British people,” he said.