In the UK you have a legal right to a minimum 14 day cooling off period on most insurance products, including pet insurance. This starts either from when you receive your policy documents or from when the policy begins, whichever is later.
During the cooling off period you can cancel the policy for any reason and receive a refund of any premium you've paid, minus a charge for any days of cover you've already had. Some insurers offer a full refund if you cancel within the cooling off period and haven't made a claim.
The cooling off period does not suspend the waiting period. Your cover starts from the policy start date as normal, and the waiting period runs from that date. If you cancel within the cooling off period you lose the cover you've had during those days but you're entitled to a refund for the remaining premium.
After the cooling off period ends you can still cancel your policy but the terms become different. Most insurers will refund a proportion of unused premium but may charge an administration fee, and the terms vary between providers.
The cooling off period is most useful if you realise shortly after buying that the policy isn't right, perhaps you found better cover elsewhere or realised you'd selected the wrong level. Its not a loophole or a way to get free cover for a couple of weeks. Its a consumer protection right that exists to give people a chance to change their mind after a purchase without being penalised.