It is absolutely worth paying the extra for warranty and backup.
What they said. I've had many, many people wheeling the remains of a Chinese made e bike to our shop in the hope of getting it fixed, only to be disappointed when we can't do anything.
The first problem is that most shops only deal with Bosch and Shimano motors, so if your no-name Chinese motor breaks after six months, you're on your own: believe me, the Anazom seller won't be interested in helping. Even if it doesn't physically break, you can't update the software, and if your display shows an error message no-one will be able to find what it is.
But that's just the start: the "cheap" bike you buy online won't just have a no-name motor, the hydraulic brakes will be non-standard, so your local shop can't maintain them, because we won't know what brake fluid to use; the brake pads will be a funny shape, and shops won't want to take the risk of liability. Wheels are often non-standard sizes, so you may not be able to get a new inner tube. If the (non-standard) kickstand breaks (which is quite likely) and the bike falls over and bends the gear hanger, you won't find a replacement gear hanger that fits... it goes on and on.
Unless you're lucky, you'll have a very heavy piece of scrap lurking in the shed (and being a fire hazard and a liability) for far longer than you ever rode it.
Buy a bike with a motor that will be serviced locally to you, preferably from a local shop, and if that's too expensive, spend the 750-1000 gbp on a good normal bike: it'll be more work, but it will still be working in twenty years.
