Ah, Animal Friends - yep they have form.
I have however just located their Policy Benefits and Exclusions and this is what they say:
Public Liability
Your legal liability to a third party, for the damages and costs arising from your ownership of the insured pet; your costs and expenses of defending civil proceedings incurred with our written consent.
Exclusions to these benefits include:
Death, bodily injury, loss or damage to you or any property owned, held in trust, the charge of or under the control of you, any person handling the insured pet with your permission and consent, any person that lives with you, any member of your immediate family, your agent or licensee, any person in the course of their employment or under a contract of service or apprenticeship with you, guest, employer or any person with whom you have a contractual or business relationship.
Death or bodily injury, loss or damage to property as a result of the insured pet’s interaction with other animals or worrying sheep.
Fines, compensation and prosecution costs following your prosecution under the provisions of the Dogs Act 1871, Dogs (Protection of Livestock) Act 1953, Dangerous Dogs Act 1991 or Dangerous Dogs (Northern Ireland) Order 1991.
Here's the link.
... and here's the link to the policy wording for their basic_prime insurance, so their lowest cost policy to include Third Party Liability
As you can see, nothing about not having the dog restrained in the Benefits and Exclusions and based on the first link and above wording, I would have said they don't have a leg to stand on and you should either contact the ombudsman straight away or contact AF again stating that you will do so if they don't agree to claim.
However, what I think they're trying to do is get you under pint 5.3.2.2 of their policy wording, which explains the exclusions of certain claims, as follows:
This policy shall not apply to liability in respect of:
any claims:-
5.3.2.2 arising as a result of any deliberate act on your part or for any other act or omission which could reasonably have been foreseen as causing the loss, damage or injury complained of;
In which case, you have two choices - Trevor Cooper or the ombudsman, because that clause is plainly ridiculous, as it will exempt just about any accidental circumstance you can think of.
So sorry they are messing you around like this. Unfortunately pet insurance is an absolute minefield and many insurers will do everything in their power to wriggle out of their responsibilities.