The sister of murdered British MP Jo Cox has said she does not want her name to be used for political point scoring.

Kim Leadbeater was speaking after British Prime Minister Boris Johnson claimed the best way to honour Ms Cox was to "get Brexit done".

The 41-year-old politician was killed by a far-right terrorist in June 2016, during the EU referendum campaign.

Thomas Mair has since been sentenced to life in prison for the attack.

Meanwhile, British Labour MP Jess Phillips has said she feels "jumpy and worried and frightened" after a man was arrested outside her constituency office on Thursday and she received death threats overnight.

"I feel desperately upset," she said.

"As I pull up to my office my constituents are having to be turned away... I just feel like they're suffering and that's annoyed me.

"The rational part of my brain says that I'm probably okay, but yeah, I feel jumpy and worried and frightened.

"I am worried for my family, although they would tell [me] that they're fine and that it's fine," she said.

"There's at least ten people threatening me in some way or another... death or violence of some sort."

"I shall carry on serving the people. I'll be all right."

A woman holds a picture of Jo Cox as people gathered in Trafalgar Square, London in June 2016 | Image: Nick Ansell/PA Archive/PA Images

Ms Leadbeater told Newstalk Breakfast she wants to see a change of behaviour.

"It was very upsetting for us - mom and dad have been very upset, I've been on the phone to them all week.

"It's really difficult to hear Jo's name being used again, but it's also very important that nobody forgets what happened to Jo.

"But what I don't want is Jo's name to be used as either a way of silencing debate - because she was a huge advocate for passionate discussion and robust debate - nor do I want Jo's name to be used for political point scoring.

"So I think that that is what I would say to everybody in the House of Commons at the moment."

Asked whether Mr Johnson should apologise for his comments, Ms Leadbeater said: "It was a very heated situation - lots of things got said, we all say things in the heat of the moment.

"I don't need a personal apology; I mean it doesn't change anything from our perspective.

"What I'd actually be much more interested in would be seeing a change of behaviour, and seeing a change of the way that things have been done going forward."

She added: "And also remembering that several of the MPs who spoke the other night - the female MPs in particular - are genuinely scared.

"There are death threats, there is abuse - and not just of the politicians themselves, but of their staff and of their families.

"Our thing as a family is I would not want any other family to go through what we've been through, and continue to go through".