The UK and Belgium have been historically very close as British strategic thinking traditionally placed a great emphasis on preventing any major continental European power from taking control of the Belgian coast opposite the British isles. That is partly why the UK went to war with Germany in 1914 when Germany invaded Belgium in violation of Belgium's neutrality.
All Belgian kings before Albert II were made Knights of the Garter and, during King Baudouin's reign, there was a Belgian state visit to the UK and a return state visit by Queen Elizabeth II to Belgium. Queen Elizabeth II also attended King Baudouin's funeral and she seems to get along quite well with Philippe and Mathilde, who visited her privately more than once in the UK.
If it were not for the current Brexit tension and, as Stefan said, the upcoming elections in Belgium (and possible early elections or a second referendum in the UK), I believe a Belgian state visit could be considered. I am pretty sure the Queen would personally like that.