I think as long as you pick up the poop it's ok - although I haven't seen parks where dogs are banned, just where they have to be kept on a lead.

I got asked to put my bc on the lead by a grumpy old sod - right outside my own house .

There is a sign as you walk down our road stating that dogs are to be kept on the lead (it's in a vineyard) but as a resident I ignore it .