The producers arrange all the permissions for them in advance - they're provided a list of places that they can sell, all of which they already have permission for.
As for the legality of what they are selling - obviously they are by and large left to make their own mistakes, but the producers intervene if any laws are being broken. For example, if there is anything wrong with what they are preparing and it is unfit for human consumption, they'll be told - like Francesca's mistake with the beer in Series 9 and the calamari going off last week. Also last year James had made a dishonest sign in the candle task (it implied that the candles had been marked down from a higher price, when in fact they hadn't been) and Karren instructed him to change it.
The candidates are left to make their own mistakes, but there are situations where interventions will be made.
