I think they'll laugh at you for £10 a chair, to be honest.
I did 52 chairs a little while ago, seat and one sided back pad. All in one room (a village hall) with plenty of space to work in. I charged £4 per chair and it was at least as profitable as carpet cleaning, and the chairs were very grotty too - thorough pre-spray & extraction needed, not just a quick "whip over". I'll charge them similar next time but benefit from having less work to do for my money

I'd have gone in a little higher if it was on a different job and the chairs were all in different places. These chairs I cleaned would cost about £22+VAT to replace, that was the first thing I checked before quoting!
As said above DO NOT underestimate the handling of the chairs!! You'll probably end up picking up and putting down each chair at least 4 times by the end of the job. It all adds up!
I prefer to line up two rows of 5 chairs facing each other, spaced out a little bit. Then go along them vaccing, pre-spraying and extracting.
You can choose to either get a sore back by standing behind them and leaning over to do the backs, or sore knees and wrist-ache by kneeling down in front of them to do the backs, using horizontal extraction strokes

The most annoying thing about cleaning small chairs is that the bloody things move around whilst you're trying to clean them. The ones on castors do my head in! I've even considered making some sort of jig to put them in so they can't move! That starts to really pee you off after about the 30th chair.
Good luck
