The letter, which is also signed by Andrea Egan, the new head of the UK’s biggest trade union Unison, says: “The British public believe in fair play: that if you work hard, follow the rules and contribute, that government should tread lightly on your life.”
It adds: “The proposals to change settlement rules would pull the rug from under migrant workers, including in social care who provide dignity and comfort to our loved ones, often in difficult conditions and for low pay.
“The government must uphold its promises – we cannot simply change the rules halfway through an agreed process.”
The letter warns there are already thousands of vacancies in social care and the proposals “risk pushing the sector closer to breaking point”.
It calls on the government to “immediately rule out applying new immigration rules to migrant families already in the UK” and for a consultation process on the proposals, which closes at the end of Thursday, to be halted until a full impact assessment is published.
Labour MPs who have signed the letter are mostly on the left of the party and it was coordinated by Neil Duncan-Jordan, the MP for Poole who has called for the prime minister to resign over the Lord Mandelson scandal.
Other signatories include Alex Sobel, a leading member of the centre-left Mainstream group, former shadow chancellor John McDonnell and Rachael Maskell, who led a rebellion against benefit cuts last year.
Former Labour leader Jeremy Corbyn, Plaid Cymru Westminster Leader Liz Saville Roberts and all four Green Party MPs are also among those who signed the letter.
Concern over the plans among Labour MPs has been growing, with around 40 criticising the proposals in a recent debate in Parliament.