Crewe and Nantwich MP Laura Smith is one of six members of Labour's frontbench who have resigned over the party's stance on Brexit.
She has quit as shadow minister for the Cabinet Office, and is the most senior of those who resigned.
Thank you so much to @jeremycorbyn. I will continue to support from the backbench— Laura Smith MP (@LauraSmithMP) June 13, 2018
In a series of tweets Ms Smith, the MP for Crewe and Nantwich which voted to leave the EU, said she was "tired of being told that I am 'blocking Brexit' by criticising the government's approach to negotiations".
She said she voted against remaining in the EEA.
"I will not vote for any amendment to Brexit legislation that does not deliver the exit from the European Union that my constituents voted for," she tweeted."It isn't acceptable to label the majority of my constituents as racist or to suggest they didn't know what they were voting for, it is not the place of politicians to tell the people they were wrong."
The resignations of Smith, Ged Killen, Ellie Reeves, Tonia Antoniazzi and Anna McMorrin on Wednesday night were revealed moments before the result of a vote on a Lords Brexit bill amendment which called for the government to make remaining in the EEA a negotiating objective.
The government said before the vote it disagreed with the amendment and the Labour frontbench had been ordered to abstain.
The House of Commons voted 327 to 126 to reject the proposed amendment, with 74 Labour MPs rebelling against their party's whip to vote in favour of European Economic Area membership.
A further 15 Labour MPs rebelled in breach of the abstain order to vote against EEA membership, while one Labour MP, Susan Elan Jones, also defied the party's official position to act as a teller for the vote.
Rosie Duffield then became the sixth Labour MP to quit her frontbench role.
Labour leader Jeremy Corbyn said: "I would like to thank Laura, Ged, Ellie, Tonia and Anna for their work with the Labour frontbench.
"I look forward to working with all five in a Labour government that invests in all our communities and gives real hope to our people.
"I understand the difficulties MPs representing constituencies which voted strongly for Leave or Remain have on the EEA amendment to the EU Withdrawal Bill.
"The Labour Party respects the outcome of the EU referendum and does not support the EEA or 'Norway model' as it is not the right for option for Britain.
"It would leave us with next to no say over rules we have to follow, it does not allow us to negotiate a new comprehensive UK-EU customs union and it fails to resolve the Irish border issue.
"But we are not voting with the government on this amendment because the Conservatives offer no plan for securing the full tariff-free access to the EU's internal market, which is so vital for jobs and living standards in our country."