I thought I'd check this out (something you seemingly didn't bother to do) and this relates to a story from 2010 when Kinnock was living in Denmark but working in Switzerland.
In June 2010, the Danish tabloid newspaper B.T. accused Kinnock of tax evasion.[12] At that time, he was paying tax in Switzerland where his workplace was situated, and where he had declared his main residence, although his wife's political website stated that "The family lives in Østerbro in Copenhagen".[13] The couple had previously stated to the media that Kinnock would spend his weekends in Denmark, sometimes including Thursday, and that he regarded his home and base as being exclusively with his family in Copenhagen. According to the newspaper, he would possibly exceed 183 days a year in Denmark, meaning he would be fully taxable there. His wife rebutted the accusations but said the couple would ask the Danish tax authority for an audit.[14][15] The audit was concluded on 17 September 2010, and concluded that "Mr Kinnock does not have tax liability for 2007, 08, or 09, as he does not reside in this country within the meaning of the Danish Tax at Sources Act"
He became a UK MP in 2014.
It's bullshit.
It does relate to 2010, but it's murkier than Wiki suggests. His Danish wife alleged for tax purposes he only spent 33 weeks in Denmark each year. But when she applied to have him named as joint owner of their house in Denmark, she claimed he spent every weekend in Denmark. When this was revealed, the Kinnocks said this was a simple mistake.
Yeah, right
Apparently the need to evade tax to pay for their daughter's private education.