Conservative MPs warning of “entryism” in their party have faced a backlash from colleagues, who say the party should welcome an influx of new Brexit-supporting members.

Leave.EU, the campaign group founded by businessman Arron Banks, is calling on its supporters to join the Conservative party to influence a future leadership vote, leading some remain-supporting MPs, including Anna Soubry and Nicky Morgan, to call for vigilance.

But Robert Halfon, the MP for Harlow and chair of the Commons education committee, dismissed those fears on Wednesday, and suggested Soubry and her allies instead recruit supporters from their own wing of the party.

“We must be the only party in history complaining because we have more members,” he told the Guardian. “Seventeen million people voted to leave: 68% in my constituency. Not many of them were robots of the Leave movement.”

He said membership in his constituency party had increased by 24%, but he regarded that as a positive sign. “Even if they are Brexit people, the idea that Arron Banks has put a little chip in them is ridiculous.”

Ben Bradley, the MP for Mansfield, who resigned as a deputy chair of the party in protest over the prime minister’s Chequers deal, said he had also seen local membership rise since he took the seat from Labour at last year’s general election.

“Obviously our town voted 71% leave, so leave voters joining would not be ‘entryism’ – it’s very reflective of our local population and local views.” He added: “I’ve seen nothing to suggest it’s anything more than us continuing to grow support locally as we have done for a year or more, no evidence it’s an ‘infiltration’ or anything like that.”

Banks himself was refused membership earlier this month but continues to spearhead a bid to persuade Eurosceptics to join the Tory party.

Jacob Rees-Mogg, one of the pro-Brexit candidates favoured by Banks and his allies, has disowned their efforts, saying: “They’re not doing it in my name. Of course I want people to join the Conservative party, but I want them to join because they support a broad swath of values.”

Meanwhile, chairs of local Conservative associations are being reminded to check new members regularly and weed out those “whose declared opinions or conduct shall, in their judgement, be inconsistent with the objects or financial well-being of the association, or likely to bring the party into disrepute”.

In a letter obtained by the Guido Fawkes website, the party’s head of membership, Natalie Crosby-Jones, reminds constituency chairs that they have an obligation to scrutinise members before confirming their membership on the party’s internal system. “Please check these individuals carefully before you click ‘Approve’,” she wrote.

With Theresa May facing an intensely challenging six months, and a growing number of her own MPs restless about the Chequers deal, the prospect of a leadership contest looks increasingly likely. Grassroots members would then have the final say, after MPs whittled the candidates down to two.

When asked en route to South Africa earlier this week about whether she would step aside if she faced a vote of no confidence, May insisted she was “in it for the long term”; but few in Westminster expect her to stay on much beyond March next year, when Britain is due to leave the EU.

Campaign groups on both sides of the Brexit divide are readying themselves for the battle ahead, as negotiations in Brussels reach their final months.

Former Ukip leader Nigel Farage emailed supporters of Leave Means Leave, the hardline Brexit group he recently joined, summoning them to a rally in Bolton in September.

“We need to mobilise and do whatever it takes to get the Brexit we voted for. We need to pressure the government into chucking Chequers and supporting a world trade deal,” he said.

“I want to see a bigger crowd than the remainers can produce. We’ve got to show them we mean business,” he said. Tickets to the rally are £5.