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Lost the back door key to my shop. How do I get it open? Destroying the lock is ok but not the door! Any ideas?

Call a locksmith....
Where was the last place you had the key?
It's a back door, obviously you've got to smash it in.
Traditional locksmith or a joiner, then reinforce any damage after. good luck.
Door doesn't look in great shape. I'd try a hacksaw blade between the door and the frame or knocking the pins out of the hinges (looks like it opens towards you so you should be able to see the hinges), or even grind off the hinges, they'll be easy to replace.
Pins out of the hinges then remove & replace the lock (and probably hinges) is favourite for me
Edit - I have done this successfully
Is that faerie's house?
Rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrgh!
Did it budge?
Hinge pins as others have said, but it shouldn't be hard to pick a mortice lock that looks to be older than my mother. Is that thing even levered rather than just warded? Might be able to open it with a screwdriver.
To be brutally honest though it looks like you'd be doing it a favour by stoving in the door.
A hardpoint saw will cut through brass and any hardened pins in the bolt, will trash the was of course though.
Wait, what evidence do we have that it’s yours? Everyone here could be an accessory to a crime...
Door looks knackered to be fair. You could park your bike in that gap.
Smash it to bits and fit a new one and leave a spare key under a flowerpot or fake pebble with a cupboard in it.
Door opens inwards, so easiest way is to drill a series of holes down the frame over the bolt, find the bolt by shining a torch between door and frame, then gently prise the door open, then just spice a new piece of wood into frame a few inches higher and lower than the damage and fit a new reciever for bolt and some big tower bolts top and bottom.
Is that faerie’s house?
I chuckled 👏👏
My pre-ride cuppa 2p musings are.
1) Top lock has key snapped in - unscrew guard plate and grip the bit of the key that protrudes with a Mole-wrench, turn clockwise.
2) The door latch plate on the frame indicates this door opens towards the person taking the photo. Giving the door a shove will not work.
3) The bottom lock appears to have zero use. Filler knife down door gap would/could reveal no actual lock and confirm top lock used. A hook behind lock would/should flex door showing no lock.
Good luck.
One of my favourite threads was the Safe opening thread.