From the Blue Cross website:
“Dogs on leads
There is no blanket law requiring dogs to be kept on a lead in all public spaces. However, there are a series of orders that mean you have to leash your dog in certain places in your local area, for example children’s play areas, sports pitches, roads, parks and beaches.
Many local authorities have introduced Public Spaces Protection Orders over the last couple of years to restrict dogs to being walked on lead (or excluded from the area entirely) in certain public spaces. Look out for signage detailing restrictions. We also recommend checking your local council’s website for details of any restricted areas.
What can happen if I break this law?
Local authorities have the power to introduce these orders under a number of different laws, and can issue fines or fixed penalty notices for those who don’t comply.
Law: Road Traffic Act 1988, section 27; Anti-social Behaviour, Crime and Policing Act 2014”
I’d recommend learning that last bit off by heart ready to quote back at the solicitor...
Might be worth checking your local gov. Website, too - the local laws regarding dogs on leads will clarify if your park is allowed to have dogs off lead, and regulations can change over time - so the solicitor might not be up to date with the current ones.