Conservative rebels have warned the Brexit secretary, David Davis, that they are “deadly serious” about forcing concessions from the government on the EU withdrawal bill.

As the leader of the House of Commons, Andrea Leadsom, announced that the key piece of Brexit legislation would come back to the Commons on 14 November, former education secretary Nicky Morgan warned Davis not to expect an easy ride.

More than 300 amendments to the government’s key piece of Brexit legislation have been tabled, and Tory MPs hope to force concessions on key issues including parliament’s right to vote on any final deal.

Davis was forced to appear before MPs on Thursday and reiterate his pledge to give parliament a vote, after appearing to suggest on Wednesday that it could come after Britain had already left the European Union.

Morgan told him, “reports have reached government backbenchers that the secretary of state does not think that those Conservative members who have signed the amendment are serious about supporting it if we need to.

“May I tell him that we are deadly serious? It would be better for all concerned if the government were to adopt a concession strategy and have the withdrawal agreement secured by statute sooner rather than later.”

In a tetchy exchange with his Labour shadow, Keir Starmer, on Thursday, Davis repeated the promise made by his junior minister, David Jones, in February that MPs would be given a vote. “The choice will be meaningful: either to accept that deal, or to move forward without a deal,” he said.

“Clearly we cannot say for certain at this stage when this will be agreed. But as Michel Barnier said, he hopes to get a draft deal done by October 2018 and that is our hope as well.”

Starmer replied: “What a mess – one thing one day, another thing the next. Today he says the vote will be before the deal is concluded – that’s not good enough.”

Asked by Labour MP Seema Malhotra during a committee hearing on Wednesday morning when he envisaged parliament would be given a vote on the future relationship with the EU, Davis said discussions could go on until the final minute of the final day of negotiations.

When Malhotra asked if that could mean a vote coming after the UK formally exited under the article 50 process timeline, which would be 29 March 2019, he said: “Yes, it could be. It can’t come before we have the deal.”

The promise of a meaningful vote was one of the key concessions made by the government during the passage of the article 50 bill in February, when it faced the prospect of a defeat over MPs’ insistence they must be given the chance of rejecting the deal.

The spat comes as the government prepares to bring the EU withdrawal bill back to the House of Commons next month. Backbenchers have tabled hundreds of amendments.

As well as a vote on the final deal, issues covered in amendments include devolution and the scope of “Henry VIII powers” that allow ministers to amend EU legislation without full parliamentary scrutiny as they bring it into British law to prepare for Brexit.

The Brexit minister Steve Baker also suggested on Thursday that the government may need to pass separate legislation to cover a transitional period after leaving the EU.

Baker said the withdrawal bill currently going through the Commons was not aimed at covering the implementation period laid out by May in her Florence speech, although MPs have tabled amendments seeking to enshrine a transition arrangement into law.

Speaking at a select committee hearing, Baker said the current legislation was “not about the transition period”.

“This bill is about how we leave the European Union and get our statute book ready for exit day,” he said. “Its purpose is to deliver certainty and continuity as we leave; its purpose is not to implement the implementation period. If we find we need to bring forward additional legislation then we will do so.”