We have the same situation- a house converted into 6 flats with a common parts area. We realised 10 years ago that this was a legal requirement and put it into place annually from then. There is a company we use who carry it out each year. I just Googled for companies in our local area.
I don't know how much you have looked into this but the FRA scope includes:
The FRA only applies to the common parts - entrance to the block, hall, stairways etc and access from the flats to the common parts i.e. each flat must have a self-closing approved fire door.
The interior of the flats are deemed to be the tenants responsibility but we require each flat to have a heat detector which will activate the main fire alarm system in the common parts plus a separate smoke alarm not connected to the main system.
Inspection of the main fire alarm system and it requires evidence that the system is maintained and has had regular tests and that the tests are properly documented. Also that the system emergency lighting works. These should have been checked by a qualified electrician and certificates issued.
All appropriate signage is in place and clearly visible at all points (directions to the fire exit, location of assembly point, no smoking).
A check that the common parts are free of obstructions.
Identifying any potential fire hazards.
There are an adequate number of fire call points properly located.
We receive a report c. 40 pages detailing required actions and recommendations at around a cost of £200.
Another survey you are legally required to carry out is an asbestos survey, usually this is a one-time survey.
Hope this is of some help.