There is definitely no regulations or legislation prohibiting this ridiculous idea.
The fire risk assessment will definitely need to be reviewed and control measures introduced to protect the public - many of who will be drunk, some will be wearing highly combustible clothing and hairspray etc. Its a disaster waiting to happen.
I did a FRA on a Korean restaurant in Soho. Each table has its own hob (and extractor above) so punters can cook their own food. I was not expecting that!!
There was no way to control the risk other than providing a warning on the menu and additional staff training. We also added discreet fire blankets in the restaurant.
Like the pub in the OP's question, the local authority have to consider fire safety when issuing a licence, so I would have a chat with them if you don't wish to approach pub management directly
