The Brexit secretary, Stephen Barclay, has warned MPs who are seeking an extension of article 50 in order to avoid no deal that the UK may not get European agreement to delay the exit date.

Overnight, six amendments to Theresa May’s Brexit plan were tabled by backbenchers, including one by the home affairs select committee chair, Yvette Cooper, which would give parliamentary time for a bill that could force ministers to seek an extension of article 50 if there were no deal.

On Tuesday morning, Barclay said MPs attempting to force an extension could create difficulties for the government with Brussels. “It is not in the unilateral gift of the UK to extend. There are practical issues,” he told BBC Radio 4’s Today programme.

He said supporting an extension was “an oversimplification” and that there was concern in Brussels about the prospect of an extension and what it would mean for the European parliament elections.

“But also from the EU point of view, they have been very clear that they don’t want an extension with no purpose and so we come back to the issue as to what it is MPs are for and just what they are against.”

The attempt by Cooper, backed by the former Tory minister Nick Boles, is the one most likely to attract frontbench Labour support.

The Labour leader, Jeremy Corbyn, has also tabled his party’s own amendment, calling for the government to put in place a process for finding a parliamentary majority for possible Brexit options – including Corbyn’s own policy, which proposes the UK remain in a post-Brexit customs union with the EU, and a “public vote”.

The shadow business secretary, Rebecca Long-Bailey, said the amendment did not “in any way” mean the party backed a second referendum. “If it was passed, the amendment, and it went to a vote on the specific issues, then that would be a decision for the party to take at the time,” she said.

Other amendments also pave the way for possible “indicative votes” on Brexit options, including one by the Brexit select committee chair, Hilary Benn.

The former attorney general Dominic Grieve has also put down an amendment signed by seven Conservatives – a sign it could pass if Labour gave its support. His amendment would mean motions by MPs on Brexit options would be given priority in Commons time.

Grieve has dropped the more controversial aspect of the amendment when it was first drafted, which had stated that any motion put forward by a minority of 300 MPs from at least five parties – including 10 Tory MPs – should be debated as the first item in the Commons on the following day.

Another amendment has been tabled by the Labour MPs Lisa Nandy and Stella Creasy calling for a citizens’ assembly, and one other from the business select committee chair, Rachel Reeves, on extending article 50.

Amendments to the motion are not legally binding but will have serious political effect. The Tory backbencher Andrew Murrison is understood to be in advanced discussions about tabling an amendment time-limiting the backstop, after hearing May tell the Commons that “the length of the backstop was being actively considered”.

Should he decide to table an amendment, it may call for a five-year limit as suggested by the Polish foreign minister on Monday. Murrison had attempted to table an amendment to the prime minister’s Brexit deal last week, putting a time-limit on the backstop, but it was not selected by the Speaker, John Bercow.

Tory and DUP MPs who had voted down May’s deal hinted on Monday night that some could be won over in the coming weeks. Nadine Dorries, a prominent Tory Brexiter, claimed she and her colleagues were beginning to reconsider, given efforts of other backbenchers to push for a second referendum or a delay to Brexit.

“I can feel a growing consensus among a number of MPs, faced with these Europhile kamikaze MPs, who really don’t care about their careers going up in flames, who want to overturn parliamentary tradition in order to stop Brexit,” she told Newsnight.

“I think many people are now realising that we would support this deal to get it over the line. Because every day here is a dangerous day at the moment. We may have to see that this is a deal, we will have to swallow our pride, swallow what we would prefer, and vote for it.”