The NHS is urging the government to relax rules on skilled workers being granted visas as hospitals are struggling to cope with the lack of doctors from overseas.
The Home Office grants more than 20,000 Tier 2 visas to skilled migrants from outside the European Economic Area (EEA) each year, with a monthly limit of around 1,700 for NHS employers.
In each of the past two months, the limit on the number of applications for Tier 2 visas was reached, resulting in a number of doctors being blocked from entering the UK.
It is reported Home Office officials were rejecting doctors who did not work in specialisms with particular shortages or those who earn less than £55,000 a year.
The University Hospital Birmingham NHS Foundation Trust said it has been forced to reject at least 18 doctors recently because they did not earn enough.
Danny Mortimer, chief executive of NHS Employers, said: "NHS organisations are increasingly concerned at their inability to obtain permits."
A Home Office spokesperson said: "It is important that employers look first to the resident labour market. We estimate that about a third of all Tier 2 [visa] places go to the NHS."
Concerns about staff shortages in the NHS have been raised since the Brexit vote as the number of migrants applying work in the NHS since the referendum has drastically fallen.
The British Medical Association warned last September that there is a "chronic shortage" of doctors across most areas of medicine in the UK and called for a flexible immigration system post-Brexit so that it can recruit and retain enough doctors.
A BMA spokesperson added: "The UK needs EU nationals who make up nearly 7% of the UK medical workforce. Any drop in numbers will only further exacerbate recruitment challenges."
Dr Chaand Nagpaul, BMA council chair, said: "We know that many doctors are struggling with unsustainable workloads in an NHS that is understaffed and chronically underfunded. This has a huge impact on their morale and wellbeing, often leading to stress and burnout.
"Brexit also poses a new risk, with almost half of EU doctors considering leaving the NHS following the referendum result.
"With the NHS at breaking point, if the government doesn't get to grips with this workforce crisis, the NHS will struggle to attract and retain highly trained staff, and patient care will suffer as a result. Ignoring this staffing crisis creates to a vicious circle, compounds existing problems, adding to pressure on existing staff and making them more likely to leave."