Low-skilled workers in sectors such as construction and social care will not be exempt from new immigration rules after Brexit despite staff shortages, Priti Patel has told ministers.

The home secretary made clear at cabinet on Tuesday that there would be no “carve-outs” under the points-based system. Although people in “shortage occupations” may be given more points under the Australian-style system, there will be no guarantee that they will be able to enter the UK.

There have been warnings that Britain will face a shortage of social care workers if care homes are unable to recruit enough staff from overseas. Ministers have also said that foreign construction workers should be given special treatment to ensure that Boris Johnson’s pledge to “level up” the country