Axa has left the pet insurance market, leaving many customers facing huge premium price hikes.

Up to 10,000 Axa pet insurance customers are being moved to NCI Insurance as Axa leaves the market to concentrate on "key products" – motor, home and travel cover.

By August 30 2015, all customers will be shifted on to NCI's insurance books.

NCI told MoneySavingExpert that it would provide "similar levels of cover" to Axa, and will "continue to insure any medical conditions identified while customers were with Axa under the terms and conditions of the new policy."

But a number of customers who have already been moved to NCI say they are facing huge price hikes, particularly for cover for pre-existing medical conditions.

Many insurers will refuse to cover animals with pre-existing medical conditions, however, pet owners who want the most comprehensive type of pet insurance will need to opt for "lifetime" cover. Insurers will set a high maximum amount per year – say, £10,000 – but you will still have to renew the policy each year, and some insurers can refuse to renew it.

One Axa customer, who has two English springer spaniels, was told that the premiums for one of her dogs, which has a pre-existing medical condition, would increase from £357 a year to £1,927 a year.

She told MoneySavingExpert that she felt she had no choice but to renew her dog's policy with NCI as she knows other insurers wouldn't cover his medical conditions, but that she has had to put her wedding on hold to pay for the policy.