I ended up having my own system designed and built to take care of this (I toyed with the idea of making it a commercial venture but haven't really pursued it ) but it genuinely annoyed me that there are no companies which just sell a box and that they all want ongoing service contracts. It took me more than two years but I eventually got what I wanted.
My system requires staff to input their numbers to a box when they get on site (no telephone line required since I do a lot of common parts cleaning and no mains power required for the same reason) and I get 1. a log of hours worked at the end of the week and 2. an automated (and free!) unlimited escalation procedure when cleaners either come in late or dont come in at all. In addition, holidays and sickness are requested and reported by SMS which removes paper filling and maintains records to allow for cover and accurate record keeping. Good news on that, if you're patient, is that I'm currently looking at ways to make that particular aspect of the service available for other companies to use free of charge since I think it's a useful tool for companies like mine. I'm expecting final build of the larger web page (which includes access to cleaners to download their payslips to save me postage) by March so that it ties in with the new tax year so if you're interested then keep an eye on this page which is the first place I'm going to announce it.