Don't price based on what you think the agency is charging. They have a proper little earner with two people just left on site all day every day.
You will be best to give a price per cabin, you can vary by style if required.
If you haven't already then go take a look at the job, talk about required spec and price based on what you need to charge.
You have already said they are providing a terrible service so why try to beat them on price alone, push the service aspect.
Last time I used an agency we were paying £7.98 + VAT but this went up to £8.50 + VAT as I recall. The problem with agency is that in a lot of cases, especially lower paid work such as cleaning, is retention of staff. We even had one person get a call whilst in the middle if a shift offering work and they've left there and then.
Bottom line is you go in and sell quality and consistency. Build a relationship from the outset and maybe offer a single clean FOC so they can see whet they'll be getting.
Good luck