BS9999:2008 recommends for fire doors with cold smoke control that the threshold gap should be either less than 3mm in height or should be fitted with a threshold seal.

I work in a relatively new office buiding that has internal fire doors (with cold smoke seals), and the gaps under the doors range from 5mm to 10mm. 

Im aware that BS are not a legal requirement but if the fire service were to make a visit would they insist upon remedial to reduce the gaps. 

The fire risk in the office is relatively low, fire detection in place, travel distances are short...

Thanks in advance

BS 9999:2017 does not seem to specify a gap just reference to the principles of BS 8214:2016

I would task the question back to the designer

For general fire doors (eg FD30) it's generally accepted that a threshold gap of up to 8mm is acceptable, but I would contact the door manufacturer to to see what their recommended threshold gap is for that particular design of door.