Hi, another heating engineer here hoping to help.
Is the thing overflowing or just running through like it's not stopped flushing properly ?
If it's the later it will be the washer on base of flush mechanism.
Some mechanisms ( most actually ) twist and come out but some you need to take it out of cistern ( if it's close coupled the cistern needs to come off) the washer may be available at plumbers merchant if not you'll need to replace the mechanism!
Sorry to waffle, hope I've made some sense