The Liberal Democrats’ leader, Jo Swinson, has been accused by Labour of not properly investigating an activist who claimed one of their MPs had made up her experience of racism.

Swinson said it was right that Steve Wilson, the husband of parliamentary candidate Angela Smith, had apologised to the shadow equalities minister, Dawn Butler, for writing on social media that she had lied about her experience of racism in the House of Commons.

In a letter seen by the Guardian, Swinson said she believed Butler encountered racial discrimination and that Wilson’s apology had been “essential”. However, she was criticised for not suspending him or revealing whether he faced any kind of disciplinary process. Butler is also demanding Wilson and Smith undergo diversity training.

The shadow equalities minister, who is one of Jeremy Corbyn’s most senior allies, said: “It has taken almost three weeks to get a one-line apology from Steven Wilson, which demonstrates no understanding of why what he said was unacceptable. Jo Swinson is refusing to say what disciplinary action will be taken against him and refusing to confirm whether he and Angela Smith will be required to attend equalities training.

“By protecting a white man who denied a black woman’s experience, the Lib Dems are actively condoning racism in their party and promoting it in wider society. Steve Wilson should be suspended from their party immediately.”

The Labour MP wrote about her experience of being a black woman in politics when she first entered parliament in an opinion piece for the Metro in October as part of Black History Month.

She wrote: “I still remember the shock when I got in a lift and was told that ‘this lift isn’t for cleaners’. It stunned me. Such blatant racism from elected members of parliament stopped me in my tracks.”

In a reply to a post Butler made on Twitter sharing the article, Wilson wrote: “Sorry but this is just not true. I’ve worked in parliament for 15 years and the lifts have always been for the use of everyone. Only time MPs have priority is during a division. Stories like this don’t do anyone any justice and anyone propagating then [sic] should stop it.”

Wilson apologised publicly after being contacted by the Guardian and has also emailed Butler, saying: “Further to recent events considering comments made on Twitter, I would like to apologise wholeheartedly for the comments I made and the subsequent offence I caused.”

His wife defected to the Lib Dems in September after quitting Labour to formChange UK. Smith represented Penistone and Stocksbridge in South Yorkshire before the election, but is now standing in Altrincham and Sale West in Greater Manchester.

Swinson personally wrote to Butler to say she believed her account of racism and that everyone has a responsibility to be “careful with the words they use”.

She wrote: “I believe we all have a responsibility to be careful with the words we use and to make sure that we are communicating in a way that is sensitive and appropriate. I understand that Mr Wilson has issued an apology for his tweet, which I believe to be essential in the circumstances.

“I want to be clear that I absolutely believe that your experience in the lift is genuine, and I think it is vital that when these experiences are shared that they are believed and not dismissed.”

She said all MPs and staff were expected to take the “Valuing Everyone” training course run in the Commons.

Butler wrote back: “This is a completely inadequate response to a complaint of racism, which is not in keeping with the Macpherson principles that instances of racism will be recorded and treated as such and investigated accordingly.”

On Tuesday, the Lib Dems contacted Butler to send her a link to a complaints form, which she had already filled out when she first complained to the party. However, they have not answered questions on whether Wilson faces any disciplinary action or if he has attended a training course on diversity.