To think direct debits shouldn't be able to autorenew if the amount has changed?

I just Googled this OP, and this was what I found

The Rules on Price Increases and Auto-Renewals

• Advance Notice is Mandatory: Under the UK Direct Debit Guarantee, the company must notify you in advance (typically 10 working days, or an alternative timeframe specified in your original contract) of any change to the amount, date, or frequency of a payment. They cannot surprise you by pulling a doubled amount out of your account without warning.

Did it not mention in the notification that it was about to auto renew, the new price? If not, then it looks like you can do something about it.

But the contract was only for that 12 months
Then it's another contract for the next 12 months...

I'm sorry but I don't see how it's dishonest

Also at any point in the policy period you can contact them to say I don't want it to automatically renew next year and they'll action that for you so it won't automatically renew next time

You don't understand what a direct debit is, do you?

That is literally what a Direct Debit is for. Maybe familiarise with the DD you agreed to when you first set it up.

https://www.directdebit.co.uk/direct-debit-guarantee/

“I had no reason to suspect they would randomly hike up my premiums like that.”

The email informing you was probably your best clue.

How do you suggest they inform you, if they have emailed you and you didn’t read it? Sky writing? Turn up at your house? Tie a yellow ribbon round the old oak tree?

The contract you 'agreed and signed on' almost certainly didn;t say that the price would remain unchanged indefinitely.

The email you received should have told you the price for the coming year (if it didn't you would have a valid cause for compaint) and gave you enough time to cancel the policy for the upcoming year if you decided you wanted to.

I agree with others in that the onus is on you to check etc etc but as it's doubled, it sounds like you have crossed some sort of threshold, like the age of the pet. Unfortunately, the older your pet the more you have to pay and this is often applied in big increments. Of course, it's also up to you to be aware of that. You could cancel this insurance and shop around for one you find more suitable.

There should be a cool off period - it shouldn't be too late to change

That is literally how direct debits work. If you want to control the amount, you need a standing order, but most subscriptions etc aren’t set up to allow that.

That's the whole point of a DD.

You had an email informing you that the price was changing. If you were busy, missed it, didn't read it- then that if your fault, not the company.

I can see its frustrating and we are all busy and can easily miss emails, BUT, the alternative could be they don't auto-renew and you need the insurance the next day/week/month then have none.

That is normal practice with direct debits IME. If you want a non- changeable amount that you set up yourself, that is a standing order. I don't think you can do that with things like insurance.
You say they sent you an email before the renewal? That is normal practice and is the point at which you look for alternatives if you haven't already done so. My home insurance renewal notice usually comes at least a month beforehand. Same with travel insurance, gas and electric, broadband, mobile phone. It is a pain but unless you can prove they didn't inform yoi I don't think there is anything you can do.
I have got wise to it all now and set calendar reminders to start looking in good time.
I am sorry you got stuck with a huge increase.

The whole point of a direct debit is that it's for a variable amount. You also admit that you got an email informing you. It's on you.