Jacob Rees-Mogg has disowned calls by Leave.EU for its backers to join the Conservative party to support him in a potential future leadership bid, warning against a takeover by single-issue “fanatics”.

Leave.EU, the pro-Brexit campaign group co-founded by rightwing businessman Arron Banks, claims to have 88,000 supporters, and has urged them to “flood” the Tory party to elect a “true Brexiteer” such as Rees-Mogg or Boris Johnson as the next leader.

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Help put the spine back into the Tory party: https://t.co/Vgc33bXJWn pic.twitter.com/GUy1UWix07 — Leave.EU (@LeaveEUOfficial) August 15, 2018

Leave.EU’s activities have prompted centrist MPs including Anna Soubry and Nicky Morgan to warn about the risk of “entryism” in their party.

But Rees-Mogg told the Guardian: “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.”

He said encouraging people to join up to back a single issue, or candidate, was “not a good approach to running a political party and its supporters, because entryists tend to be fanatics, as the Labour party has found”.

The MP added: “What the Conservative party wants is what it’s always had, which is members who are by and large already doing things in their communities – people who are running the church fete or raising money for the RNLI.

“You want being a member of the party to be a completely normal thing that sensible people do, not something that is done for one particular policy, however important that policy is. Conservatism is much broader than that.”

Leave.EU is one of the groups responsible for an upsurge in campaigning activity on both sides of the heated Brexit debate, as negotiations in Brussels approach their denouement.

With the hardline pro-Brexit European Research Group mobilising MPs to oppose Theresa May’s Chequers deal, there is a risk that the prime minister could face a vote of no confidence.

Conservative rules say that anyone who has been a member for at least three months before a contest has a vote.

Many at Westminster believe the greatest challenge for a pro-Brexit candidate such as Johnson or Rees-Mogg would not be winning over grassroots activists, but securing the support of enough MPs.

Conservative MPs whittle down the field of candidates to two, in a series of secret ballots, and members then have the final say.

The latest poll of Tory members by the website ConservativeHome earlier this month showed Johnson is currently the most popular candidate, with the home secretary, Sajid Javid, second and Rees-Mogg third.

Some activists have called for the rules to be rewritten to enhance the role of members, but Rees-Mogg said the former foreign secretary William Hague was right to argue earlier this week that MPs should continue to have a significant say.