Vintage Horticultural and Garden Machinery Club

I am not aware of any Uni-Horse clubs or groups.

There is the Lea-Francis Owners Club, which mentions the Uni-Horse, but the club generally seems more geared towards the cars that were made.

https://lfoc.org/index.php/unihorse-tractor

I hope you manage to find a tractor and a plough to continue your ploughing.