Labour is drawing up a social media code of conduct for its members and supporters, amid concerns about the way political debate has recently descended into online personal attacks.

The national executive committee agreed to start developing guidelines after concerns were raised about “the issue of the very harmful leaks to the media and the very damaging way in which social media is being used”, according to an account by one Labour member, Peter Willsman.

“It was agreed that we need to develop a Labour party code of conduct in relation to the use of social media,” he wrote. “Jeremy [Corbyn] thanked the party staff, the NEC and party members for their support in the face of a hostile attack on him personally and on the party.”

A number of Labour MPs have told of receiving personal abuse online during the leadership campaign, including the contender Liz Kendall, who was subject to sexist remarks, threats and accused of being a Tory.

Since becoming leader, Corbyn has stressed that he wants a new, kinder politics in which there is no room for personal attacks. In his conference speech he demanded that activists “cut out the personal abuse, cut out the cyberbullying and especially the misogynistic abuse online and let’s get on with bringing real values back into politics”.

However, there is fear among some MPs critical of Corbyn that the code could be used to try to prevent them and other members from criticising the party leadership on social media. Labour MPs Mike Gapes and Jamie Reed have been engaged in lengthy and bitter arguments online with supporters of Corbyn in recent weeks.

This was dismissed by Alice Perry, another member of the NEC, who said the code of conduct was about “tackling bullying and cyberbullying of party members and the importance treating everyone with respect”, rather than a move to silence critics of Corbyn.

“Everyone is in agreement that we don’t want to have personal bullying on social media, or any other forum,” she said, pointing out that MP discipline is a matter for party whips.

Another source present at the meeting said the concerns raised were mainly about ensuring those who oppose Corbyn politically, feel able to tweet their point of view without being called “Tory scum” or other insults.

The case of a non-Corbyn-supporting member who had left the party because of abuse online was cited in support of the need for a set of rules for online behaviour. The new code of conduct is still being formulated, but it was suggested that it could include a system of warnings for those who flout the guidelines.

Andrew Fisher, a policy adviser to Corbyn, was criticised by Labour MPs and suspended by the party over allegations he was rude about former members of the shadow cabinet online, as well as urging a vote for a Class War candidate standing against Labour in Croydon at the general election. Fisher apologised for the tweet in support of Class War, which he maintains was a joke, and has since closed his social media accounts.

Willsman hinted in his account of the meeting that Fisher’s suspension could soon be lifted. “I understand that the officers’ investigation is nearing completion and that the matter will be satisfactorily resolved very shortly,” he wrote.

The NEC meeting last week also agreed to take security services company G4S to task over its involvement in supplying Israeli prisons, before it is allowed to provide security for Labour’s conference next year.

Willsman wrote: “Several NEC members raised the very contentious issue of the employment of G4S at our conference. It was felt that before G4S are invited to tender they should give the party assurances on the issues of concern.

“This proposal, on being put to the vote, was carried by 12 votes to four (there were several abstentions).”