http://www.rsm.ac.uk/media/downloads/j06-06moredrs.pdf
2.3 doctors per 1000 people in 1993. Population of ~60 million
60,000,000 / 1000 * 2.3 = 138,000. Sounds about right, of course in the last year or two this should start rising pretty sharply.
That article says the OECD average is 2.9 which would place the "ideal" number of doctors at 174,000. But the UK has always had a below average number of doctors.
That article is actually very interesting, take a look at the gender distribution diagram on page 2, the number of male doctors between now and 1960 has hardly changed. Of course then there were far fewer women than men and now there are far more women than men.