A lot of it depends if it's per condition for those figures, I'm assuming it is, in which case unless the dog your vet spoke about is being treated for purely one condition the chances are the majority of their bills will be covered by their insurance, if they have a policy that is.
It's they're talking about more than £12K in a year for one single condition I would be very surprised. It is possible, but I'd be curious to know exactly what condition they are treating to create that level of bill over one year. It wouldn't be unheard of for a Dane to rack up £12K over a year for a mixture of conditions, but even then it would be a very unlucky pup.
We had an advance policy with Direct Line for £8K per condition over the lifetime of the policy. We made one claim for emergency bloat surgery (£1K) which was paid promptly and directly to our vet. We could have claimed for some others things around the £400 mark, but it was staggered over months and didn't reach a level I felt was worth paying the excess and pushing our policy price up.
I found PetPlan to be very expensive when I got quotes from them, but I've heard people say their policy price stays very steady regardless of claims (no idea if this is true). Direct Line put our policy up each year so we cancelled and then took out a new policy each year (overlapping the cooing off period) until we had pre-existing conditions that I wasn't comfortable having excluded. We were paying around £35 a month until then, and £50 after we let it renew. We lost Duke before our next renewal after his bloat claim so I can't comment on the rise after that. I removed the additional cover for things like Reward money if he went missing, purchase price back on death etc. and it lowered our premium a reasonable amount.
I would look around for some more quotes personally. Have a look at Quidco as well, you might be able to earn some cashback on whichever policy you buy. When we had insurance for our cat we actually made a profit on her policy after cashback, and we got a fair bit from taking out Duke's over the years too.