I am an Irish national and my non-EU wife and son (Indian) have EU family cards issued by Romania (long-term residency valid for 5 years). Can my son and wife travel to the UK for a few days with me to watch a soccer match?
I have an EU Blue Card and I am pretty sure that your family will need a Visa to travel to the UK. Most of the websites where you need to check the availability of Visa for travel do not state exceptions if one holds EU Blue Cards/Green Cards etc. The main basis for entry depends solely on the fact that which Passport you bear.
In a synonymous situation, if you are an American Green Card holder but you still have a passport that requires a Visa to travel to a certain country; you will still need to apply for a Visa.