You really need to drop your profit margin on this one.
As has been said, £15 p/h is fine for builders cleaning, but way too steep for compound cleaning.
£7.50 p/h for the cleaner is about right, so I would go in at about £10 p/h.
That's still around £350 pre tax/NI/holiday pay profit per month!
I think at £15 p/h you would lose this one. Better to make a smaller profit than none at all!
I would also consider not quoting by the hour, just a flat calendar monthly price.
So, at £10 p/h my quote would be £1,516.66 per month.
(35 x 52 divided by 12 x 10)
That works out at £379 pre tax/NI profit per month.
A very rough, end-of-year, after all your costs, total profit, will be around £2,000 per year in your pocket. Still not too bad for a little additonal paperwork.
It still seems a bit high to me, but I would tell the contractor to work out how much it will cost them to employ a full-time cleaner themselves, and that by using yourself, they are getting a complete cleaning service and all that entails.
Good luck...