Unfortunately this weed is becoming resistant to weed killers like glycophsphate. I think you will have a long battle to rid yourself of this one. I hope other members will give you a more optimistic solution.

Kurtail Gold is about the only effective control, but its not cheap I'm afraid.

Reading the label for Kurtail Gold, it looks like it will kill the tops of the mare's tail, but leave the roots alone, and it is not selective. Defoliate mare's tail often enough, and it will eventually give up, but that can take several years, and if it is near the property line, there will always be more creeping in from the neighbors. Here in the U.S., Halosulfuron methyl is recommended, but I don't believe that it is available in the UK.