No, UK should not intervene in Syria. I say this because the United States have intervened in various issues of other countries and for the most part nothing good has come out of it except death and confusion on both sides. Syria is their own entity and should be allowed to handle their internal issues by themselves.
Syria's conflicts are indeed heartbreaking to watch, but this is a problem they need to work out for themselves. It's a civil war, and just like the United States has no place getting involved over there, neither does the United Kingdom. Hopefully in time the warring factions in Syria can come to some sort of truce or understanding.