Sorry I'm not being very clear. Of course Piper cub training is perfectly acceptable in the UK. There are flying schools that teach on them. However if you were to mention at many flying schools that you had XXX hours of flying Piper Cubs with your father, I don't think they would be interested in the fact that you just might be capable of flying one.
Not, I might add that the CAA should be expected to credit that time for the issue of a licence, just that the flying school should respect that you are not a raw, dumb, useless rookie that has never seen an aeroplane before.
When I went to the flying school to begin the PPL course I was current on gliders, I had a share in a single seater, I mentioned that to two instructors, I didn't make a big deal about it, nor expect special treatment, but to start the lessons with demonstrating "basic primary effects of controls" I thought was a bit much. But I said no more and just went with the flow.
No doubt I'll come across here as some kind of smart ass.