I don't think the UK government would try to put Apple out of business if they don't comply it's more likely that they would just get heavily fined until they do so. The most likely outcome, I would guess, is that Apple just stop offering Advanced Data Protection as a service in the UK rather than create some kind of backdoor. It's a weak proposition from the government because anyone with something to hide will just…
The UK government can’t put Apple out of business; Apple can easily afford to simply exit all business in the UK. The UK is betting that Apple’s greed outweighs their principles. Long odds.
Apple has shareholders, so no it can't (or more precisely, Tim Cook can't).