Independent MPs will push the government to soften its pledge to cap foreign student intakes, as the lobby group for leading universities targets politicians holding marginal seats with warnings of “devastating consequences” for the $48 billion international education sector.

Proposed as a fix for the housing affordability crisis, some Labor insiders are nervous the plan to cap international student enrolments may backfire, harming the country’s fourth-largest export sector and exacerbating stubborn skill shortages from hospitality and retail to healthcare.