I work in a pub which is set over 2 floors. Main bar and customer area down stairs and then customer toilets, kitchen and staff areas up stairs. The only way up to the 2nd floor is via the main staircase. There is no other way to get out the building from upstairs should there be a fire other than the main staircase. If a fire should start on the stairs or at the bottom of the stairs all people upstairs would be trapped. Is this legal? Should there be more than fire escape from the second floor?

Assuming it's not a large building then no - the staircase is meant to be a protected stair (fire resistant walls and doors) that will resist fire and smoke for up to 30 minutes - also it should not contain combustibles or ignition sources.

There should also be a suitable fire detection & warning system.

Guidance - https://www.gov.uk/government/publications/fire-safety-risk-assessment-small-and-medium-places-of-assembly