Good point civvy- I had read it as an external but it may be a single internal staircase.
Hertsmere- You will need to carry out a fire risk assessment of the new offices.
This will take into account the size of the buildings and how far people have to travel to reach the nearest exit, the layout and arrangement of the staircases, whether the internal staircase is open plan or enclosed by materials that will give some protection to people from a fire as they leave the building.
If it is an external wooden staircase is it protected by fire resisting wals, windows and doors beneath or adjacent to it.
If the wooden staircase is in good condition, not rotten or covered in green slime, and if there is enough borrowed lighting for people to see their way down it during working hours it should be ok.