Mr Tapp penned an article asserting his belief that foreign care workers already in the UK should not face extended waiting periods for indefinite leave to remain.
Home Secretary Shabana Mahmood has called for Mr Tapp’s dismissal, accusing him of breaching the ministerial code and collective responsibility.
Downing Street has resisted these calls, confirming that Mr Tapp remains in his post.
This stand-off occurs amidst broader political turmoil, with Andy Burnham emerging as the frontrunner to replace Sir Keir Starmer as Labour leader by July 17.