Afraid not. If you can't change your allotment you are in for a struggle. The roots go down very deeply and will pierce membrane let alone mulch. Shallow hand weeding can be counterproductive.
Chemical treatment will work eventually. See this link to the RHS advice:
https://www.rhs.org.uk/advice/profile?PID=257

Thanks . Can't move plot really , so will have to share plot with the horse tail.

You need to get rid though. It will not go away on its own and will spread.