The VISA's cover a lot more than doctors but there is no shortage of people wanting to get into the medical profession, there is a ratio of at least 10:1 on admissions to medical schools.
Plus you need a lot of money and top grades to even have a chance given the capacity limit.
The medical profession is closed shop and train exactly the number they want to train, in fact a request to train more is called over-training as this article from a couple of years ago shows (http://careers.bmj.com/careers/advice/Why_don%E2%80%99t_we_train_more_doctors_than_we_need%3F)
Given there were shortages then, that is bonkers.
It costs the NHS £700,000 to train a consultant from day 1 in medical school. However no one lays out the cost of getting contractors and agency staff in which no doubt over a few years would add up to a lot more.
You could increase capacity and tie grants to working in certain areas for certain periods of time. This is not new (see Northern Exposure TV show).
Short termism has infected the NHS from the private sector and i suspect the larger % of women has not been factored in for availability as they need more part time flexibility.
The system is also under strain due to the government cutting back community care.
There is no excuse for this, the aging population demographic has been highlighted since the frickin 90s.
No planning is the same as Sh*t planning