The annual limit of 20,700 on all non-EU skilled workers, broken down into monthly quotas, has been breached every month since December.
May had promised to end EU freedom of movement after Brexit, but she has yet to publish her plans for a new immigration system.
She wants migration controlled but says Britain should also attract the “best and the brightest” from around the world.
The government has announced a new “start-up” visa for technology entrepreneurs, which will replace a visa route that was previously only open to graduates.
Migration Watch, a pressure group demanding tighter controls, reacted with disappointment to the government’s changes on doctors’ visas.
“It may be necessary, at least temporarily, to cope with the prospect of Brexit, but in the longer term the answer has to be to train our own medics and not take them from countries that need them far more than we do,” chairman Andrew Green told the Daily Telegraph. SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇