They have assured fans their split has been "amicable", ever since announcing their separation in December.
However it was reported on Wednesday that Sherlock's Amanda Abbington had been concerned about the close bond Martin Freeman had with a colleague, in the lead up to the split, the Daily Mail reports.
According to The Sun, the actress, 42, was left "furious" and "demanding answers" regarding the 45-year-old's friendship with a female showbiz researcher he often worked with.
While Sherlock star Martin has called their separation "amicable" on two separate occasions, his ex-wife was reportedly left "uncomfortable" with the actor's closeness to his co-worker.
A source told the newspaper: "Amanda was absolutely furious about it - she confronted him over his relationship with the woman, who works in the business too, and demanded answers.
"She was obviously uncomfortable with how close Martin and this researcher appeared to be - and made her feelings completely clear on the matter. It was very frosty."
However the insider claimed that while there was initial hostility over the situation, the pair managed to salvage their relationship for the sake of their two children, Joe and Grace.
"In the end Amanda and Martin's split has been very amicable," the source added. "Fortunately they've managed to move on from it and they've both stressed how much they intend to remain the best of friends."
Mail Online has contacted representatives of both Martin and Amanda for comment.
The new claims emerge shortly after Martin described their split, which occurred "in the early part" of 2016, as very amicable in an interview with the
"We split up a while ago," he told the publication. "I mean, we're very friendly and it's all lovely and cool. Yes, we've not been together for a while. I mean, we did the series not together."
During the interview, Martin, who had been with the actress since 2000, was careful not to spill too many details about the shocking split - but he appeared to be taking things in his stride.
"I'm all right, yes, I mean, we're honest to God doing it [separating] in about as civilised a manner as I've ever heard of, you know. I love Amanda's work. I think she's brilliant as an actor and she's brilliant as a woman and, yes, I love her. I will always love Amanda, but, yes, we're... you know, that's what's happened."
Martin first met Amanda, 42, on the set of 2000 movie Men Only and they went on to have a son, Joe, 10, and a daughter, Grace, eight.