As this is the UK not America I assume you mean ground & first floor premises, not first and second floor.
I firstly point out that you cannot have an L3 system if you are only using non interlinked domestic smokes and so would query the adequacy of the fire warning system first.
To help determine the necessary extent of the above I'd want to look at the state of the compartmentation between ground & first floor.
I would also be wanting to look at the need for emergency lighting (although borrowed light it still permissible in certain limited situations).
No extinguishers required to the common stair as a protected route, but the hairdressers should provide appropriate extinguishers adjacent to the storey exit, either a combination of 13A rated liquid plus a 2 kilo CO2 or the DCLG Entry Level Guide quick mix of a 2 kilo ABC Powder.
If the landlord doesn't know the answers to their query & doesn't feel competent to assess themselves with the DCLG guides them they need to employ a competent external person to do their FRA.
Not trying to be clever but does this not link to the posts about competency of fire risk assessors and the need for 3rd party accreditation??? Just a thought?? From how you describe the situation the lack of extinguishers wouldn't be my main concern?
William has a point - we only have your word that you are not selling extinguishers or an FRA and whilst you may well be genuine there are those who are not - on the fire alarm engineers forum they have had to split it into two sections with entry vetting due to problems with people who are not competent trying to get free advice to cover their inadequacies and be able to keep undercutting legit people