You’re getting too caught up with the bottle. Forget about the bottle; it’s the sauce you want. And you want to have it available without having to go have a meal just to nick some for later. So, it’s really the recipe you want.
Option 1. Go on pinterest and type "copycat (name of sauce) sauce" into the search bar. Nearly every restaurant has copycat recipes on Pinterest now.
Option 2. Find out which employee in the pub makes the sauce. Befriend them, get them rip roaring snockered and talking. You know what they say, loose lips drop recipes. Or something like that.
Option 3. Most likely, the recipe will be stored in a recipe box, a binder, or a laminated flip book somewhere in a shelf above the prep area. Break in after hours and steal it. There are no moral qualms about theft of a recipe as long as you don’t profit from it. As a penguin, it’s not like you can be prosecuted for breaking and entering. That would be mean to wildlife.
Option 4. Pay or extort someone else to do option 3. Threats may or may not be necessary. I leave that to your discretion and good sense.
Option 5. Pretend to be slobbering drunk and looking for the bathroom, walk into the kitchen and steal it yourself.
Option 6. Same as above, only you’re a distraction while your penguin partner does the nicking.
Option 8. Shower the owner with compliments of the sauce. Tell them you’re famous as a playwright and convince them to let you sign the recipe. When they bring it to you have penguin partner snap a pic of it while you’re signing.
Option 9. Get a job there and learn the recipe yourself. Then make up for the time by writing a play about fast food service. It would be a hit, believe me.

Option 10. Google your local taste savant, invite him/her to dinner and bet them £10 they can’t tell you the ingredients and proportions of the sauce. Best bet you ever lost.

Option 11. Send some to a lab to be analyzed by mass spectrometry. Recreate from there.

Option 12. Pretend to be a health inspector doing a spot inspection based on a complaint to gain access to the back. Find the recipe and memorize or take a pic.

Let me know if none of those work. I have a few more ideas but they might be a little far fetched. 😁

Also, some of those are 2 person operations. I’m a little concerned, given the discourse, that penguin partner may prove to be difficult. You may have to threaten to withhold sex to secure cooperation. Just saying.

This is an interesting and fun departure for you. Kudos. This was delightfully fun.