Leeds Central Labour MP Hilary Benn, the chairman of the Brexit select committee, has tweeted that he would not be supporting the Prime Minister's deal.
MPs will vote tomorrow on whether to back the deal with the EU secured by Boris Johnson yesterday.
The numbers are tight and Mr Johnson will spend today on a charm offensive to win round wavering colleagues.
But Mr Benn already ruled himself out.
He said: "While all the attention has been on the Northern Ireland Protocol, the really important document in this Brexit deal is the political declaration because that's where the Government has set out what kind of future relationship it wants with the EU. It's bad news.
"The free trade agreement that the Prime Minister wants will end frictionless trade and result in additional cost and bureaucracy for British businesses, and any divergence from a level playing field will adversely affect our access to EU markets.
"The Government's own economic assessment of the different options for a future relationship found that a free trade agreement would be the second-worst outcome for the economy after a no-deal Brexit.
"Negotiating a free trade agreement and everything else - eg on services, data transfer, security, foreign policy, scientific co-operation, working together on aviation safety and medicines and chemicals regulation - will take a long time. Canada's deal with the EU took 6 yrs.
"Overall, it's even worse for the economy than Theresa May's deal was. It doesn't help manufacturing or services. And it opens the door to a deregulated future. I will vote against it, and it's time for a confirmatory referendum so that the British people can decide."