His own Hawkhill Medical Centre had taken on just over 20 eastern Europeans out of 104 new patients over the last 6 to 8 weeks, but this represented less than a fifth of one percent of his practice’s 11,000 patients.

Dr Cowie said the extra appointments required were a “pain” but he believed the volume of immigrants coming to Scotland had been as big a surprise to the Scottish Executive as they had to GPs.

Concern has been mounting since the British Medical Association’s Scottish GPs committee called for extra funding to help it cope with immigrants.

The Executive calculates doctors’ budgets on the basis of the total number of patients in the country and pays out depending on what percentage of the “cake” a GP has.

Since April last year, 46,000 new patients have registered with GPs, with the BMA putting the rise down mainly to the number of eastern Europeans settling in Scotland. Some doctors claim the 46,000 figure is, if anything, an underestimate.

This has given rise to worries that doctors are being asked to do more without any extra cash being placed on the table by the Executive.

Andrew Buist, deputy chairman of the Scottish GP’s committee, said the BMA recognised the contribution the immigrants were making to the workforce but the Executive had to ensure resources were available to keep up with their ever-growing numbers.

Today, Dr Cowie told the Evening Telegraph he did not believe they would ever reach a stage where patients were being turned away from surgeries through lack of funding.

He said, “This situation shouldn’t affect patients at all. It just means doctors aren’t going to get paid for those particular patients and will have to suck up the extra work.

“Doctors will be underpaid by an amount according to the percentage of these patients they have but I can’t see that this will lead to anyone being turned away.

“It’s a matter for discussion between GPs and the Government because the population is going up. I honestly do not think the Government anticipated this would happen.”

Dr Cowie said the situation was much worse for doctors in the south of England, where large communities of asylum seekers, often suffering from ill-health, were a particular problem.

He added, “New patients tend to be a bit more of a pain, especially when they don’t speak English very well, but most of the EU immigrants are young and fit and are not that much extra trouble.

“We also have established Polish and Russian communities here and translators are available.

“The two or three extra appointments each GP might have each week is a pain but it won’t cripple the system and it is not the case that it is breaking down.

“Having said that, the 46,000 extra patients is definitely something the GPs want to sort out with the Government and hopefully we will get it sorted.”