The carrier sends all passenger details to the U.K.’s Border Force Agency which in fact do conduct criminal checks PRIOR to your arrival. It’s is their discretion to refuse entry.
To clarify the databases used, NCIC is the U.S. system, CPIC is Canadian. Interpol is primarily for transitional crimes and terrorism.
Yes, you can be denied entry to the U.K if you have a criminal record, regardless of where it’s from.