Ridiculously over invested in this thread! Hope you get him out soon.
I've read all your posts on the thread but only slim read the last 30 or so replies so apologies if I'm repeating anything.
To enter the property using powers under the Animal Welfare Act, you'd need to be either a police officer or an RSPCA inspector.
However, you would be on relatively firm ground if you caused minor damage to free your cat. There is a legal defence to criminal damage where it is to protect your own property within (cats count as property in UK law). It's also a defence to commit damage if you believe the owner would reasonably consent if they knew the full circumstances. Given the alternative is likely to cause unnecessary suffering and death of an animal (itself an offence), you could reasonably assume that.
Therefore, if it was me and I'd taken all read steps to identify and contact the owner, I'd either be trying drain rods to force the cat flap (they would be strong enough to force the cat flap open and bendy enough to cope with the curve), or I'd be breaking a small window to get him out.
Good luck!