David Cameron has been warned to stay away from Scotland during the EU referendum campaign - or risk boosting support for Brexit.

SNP sources said the Prime Minister's presence north of the border in the run-up to 23 June would damage the Remain campaign.

Opinion polls suggest Scots are likely to vote heavily in favour of Britain staying in the EU.

But one Nationalist insider said: "We need to do two things in Scotland - encourage people to vote, and make sure they vote Remain. David Cameron doesn't help with either of those things.

"It would be best if he concentrated on campaigning in the rest of the UK and didn't come to Scotland at all."

The warning came after SNP leader Nicola Sturgeon took a swipe at Mr Cameron's campaign strategy of relentlessly warning voters about the potential pitfalls of Brexit.

Speaking during a visit to Westminster yesterday, the Scottish First Minister said: "That kind of fear-based campaigning that starts to insult people's intelligence can have a negative effect.

"I have control over how I campaign and I'm going to make a positive and progressive case."

Although Mr Cameron did visit Scotland during 2014's independence referendum campaign, his trips north were tightly-managed events which rarely involved him meeting members of the public.

The Prime Minister also chose not to campaign for the Scottish Conservatives during the Holyrood election earlier this month.

Scottish Tory leader Ruth Davidson defended the decision. She said: "I've said he's quite busy right now hosting a state visit for the president of the US, he's handling the 90th birthday celebrations of our monarch, Her Majesty the Queen, the House of Commons is sitting and he's the Prime Minister of a G7 nation and he's looking to make sure the Government's proposals in terms of the referendum of Europe is headed by himself."

The strategy appeared to pay off, with the Tories more than doubling their representation in the Scottish Parliament from 15 MSPs to 31.

Number 10 tonight insisted there would be no no-go areas for Mr Cameron during the remainder of the referendum campaign.

A source said: “The Prime Minister will be campaigning right across the UK in the coming weeks and making the case that the UK is stronger, safer and better-off in a reformed EU."