In an area of a building where people are barefoot ( public swimming pool) is there any obligation on that place to provide protective footwear for evacuation to an outside assembly point away from buildings? Is the provision of overshoes or socks required?

I am not aware of any such obligation but is it necessary to evacuate outside the premises immediately have you considered horizontal evacuation?

Horizontal Phased Evacuation In hospitals, and care homes the floor maybe divided into a number of fire resisting compartments and the occupants are moved from the compartment involved in fire to the adjacent compartment and if necessary moved again. Depending onto the fire situation. Because of the extra time this type of evacuation takes, other fire precautions maybe be required. These include: voice alarm systems, fire control points, compartmentation of the premises using fire-resisting construction.

Check out http://www.firesafe.org.uk/fire-emergency-evacuation-plan-or-fire-procedure/