I don't believe smoke detectors are any code on an EICR as they are not within BS7671 - though they can be noted in comments of course. (assuming the wiring is not the problem, such as bare wires outside enclosure, etc)
They may be breaching various legal requirements if it's a rented property, but that is a separate issue from the EICR.
560.6.1 - The following electrical sources for safety systems are recognised;
I) Storage batteries
II) Primary cells
III) Generator sets
IV) Sperate feeder supply network
560.10 - Fire detection and fire alam systems shall comply with the relevant parts of BS 5839 series.
5839-6 covers domestic premises (it can be argued that a private rented home is a commercial venture so should come under the scope of 5839-1, but for the sake of argument we'll use 5839-6) so the following can be applied:
Clause 15.2 states that "
The standby supply should be capable of automatically maintaining the system in
normal operation (whilst giving an audible and visual indication of mains failure) for
a period of 72 h".
Clause 15.4d states that for a category LD2 system;
'The standby supply for smoke alarms and heat alarms should take the form of a
primary battery, or a secondary battery'.
Clause 15.4e states that for a Grade D system;
"The capacity of the standby supplyshould be suffiecent to power the smoke
alarm(s) and any heat alarms in the quiescent mode for at least 72hr while giving an
audible or visual warning or power supply failure, after which there should remain
suffiecient capacity to provide suffieicnet capacity to provide a fire warning for a
further 4 mins. In the absence of a fire, a fault warning light should be active for at
least 24hrs"
If the batteries are flat or not present then the above clauses are not met and as a result, do not comply with the relevant part of BS 5839, contrary to 560.10
It should also be noted that a fire alarm (or detector) can be classed as a life safety system and as such can attract more stringent coding, whereas a non life safety system may not - This is primarily done to 'force the hand' of the client to ensure compliance with standards outside of 7671 and shows that the duty of care placed on the Electrician has been suitably discharged.
Remember that 7671 is a minimum required, so if you can go beyond that, applying necessary engineering judgement, clients are more likely to be accepting of codes that may appear excessive.