From what I know even Bitcoin ATMs in the UK require KYC or else their service will just be limited to the people who are transacting without any KYC. I did a little research about BitAccess ATMs and also they require KYC for their transactions so I think this option isn't really what the OP is looking for.
-snip-
It's being some time since I last used their ATMs, but IIRC the limits were high (~1500 GBP per day).
Also, KYC is pretty easy to avoid here. If you think you're going to exceed the limits, just change the phone number you're using.
For people in the US, the limits are pretty horrid -- I think they're in the realm of 200-500 per ATM. Doesn't stop you from roaming around to tons of different ATM's, but still - pretty big difference between $1500 GBP and $200-500 per machine.
Guess that's what we get for the 'land of the free'