ipad bent due to swollen battery

An iPad's chassis won't spontaneously bend; a swelling battery will instead displace the screen from the chassis.

If the chassis is bent, this would suggest that the iPad has suffered physical trauma. Physical damage of this type is often attributable to the iPad being set-aside on soft furnishings (or a bed) - and is then inadvertently sat upon causing the chassis to bend at a weak point. In extremis, bending can rupture the battery.

As such, of itself, a bent chassis is unlikely to be accepted as a warranty failure. Accepting the repair at the quoted cost may be considerably more cost effective than rejecting Apple's offer and replacing the iPad with a new device.

For practical purposes, in lieu of repairing and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for repair. Unless you have benefit of an active AppleCare plan, an out-of-warranty repair while expensive will be somewhat less than the cost of a replacement iPad.

As for out-of-warranty repair costs, Apple offers a fixed-price price repair. You can verify eligibility and cost for your region/country here:

iPad Repair & Service - Apple Support

If you have an active AppleCare+ plan, the cost of repair is reduced to a small excess/deductible fee.

Presumably your iPad is out of warranty. As such, it makes no difference at all as to the cause of the iPad damage - as the cost of a non-warranty repair will be a fixed price.

Conversely, if the iPad is within warranty, a swollen battery and consequential damage will be covered by a warranty repair. A swollen battery does not magically recover its original physical dimensions when the iPad is disassembled.

In either case, warranty or not, the damaged iPad will be exchanged for a refurbished device unless your UK statutory rights dictate otherwise.

Apple will not replace the battery in a damaged/bent chassis and return it to you.

If the iPad is "repaired" by Apple with a new battery, you will receive a reconditioned iPad that will be indistinguishable from new. The original iPad will be consigned to Apple's refurbishment process where it will receive a new chassis and/or be scavenged for reusable components.

Where was this technician? Was this at an Apple Store?

Excellent - a wonderful result for persistence.