If the alarm company is talking about doors from the rooms to the corridors then they are incorrect. It sounds like they are getting muddled up with inner room requirements. If they cannot be trusted to get this simple fact right then I would not trust them to install a system.
The base requirement for such a building is a type M system, as currently installed. However, a fire risk assessor might recommend some detection coverage. If the building is occupied by people on the upper floor when the lower floor has been vacated, for example when someone is working late on the upper floor, then it would be beneficial if the person on the upper floor knows about a fire that starts on the lower floor. Therefore, many people believe that an L4 system is ideal for a building such as this. That is, detection in the escape routes only. L3 might be over the top and would probably require detection in nearly all, if not all, rooms. An L4 system would give flexibility to the use in the building by providing early warning for people when other people are not there to raise the alarm.
An L4 system, ironically, would also deal with the issue of smoke getting into a corridor and affecting people's means of escape from the rooms (as alluded to by the alarm engineers) - but this is not essential and no UK codes recommend it - by virtue of the fact that experience has demonstrated that this potential problem is seldom, if ever, realised.
I recommend looking for another quote and considering the benefits of an L4 system (it probably wouldn't be required if everyone who works in the office building gets in at the same time and leaves at the same time, for example). Consider also coverage for inner rooms and dead ends.
Stu