Theresa May is expected to lift the cap on doctors from outside the EU within weeks after the NHS warned it is leading to staff shortages, The Telegraph has learned.

The Prime Minister previously blocked plans to relax the visa rules when pleas were made by Amber Rudd, the former Home Secretary. However she is now preparing to lift the cap to meet the NHS’s needs.

Discussions in Government are at a "fairly developed stage" after Jeremy Hunt, the Health Secretary, and Sajid Javid, the Home Secretary, persuaded the Prime Minister to relax the restrictions.

Government sources told The Telegraph that discussions are focusing on the precise mechanism for lifting the cap on "tier 2" visas for highly-skilled workers, which currently stands at 20,700 a year.

The move represents a softening of the Prime Minister's tough line on immigration and comes ahead of the 70th birthday of the NHS next month.

The Prime Minister has faced a series of public challenges over her approach to immigration, with a string of Cabinet ministers urging her to drop her target to reduce the number of people coming to the UK to the "tens of thousands".