You mean when the national living wage rises, and ipso facto, so do their rates? Or do you mean rises along with inflation?
What about rewarding them with pay rises when they don't ask? They provide an extremely valuable service to you and should be rewarded for the hard work, no?
Out of interest, are you paying a salary, or by the hour? What benefits do they get? What is the actual rate you pay them?
No one, and I mean absolutely no one, is going to the effort of 'signing on' (and all that entails - you do actually have to do some work to receive benefit money you know - the government doesn't make it easy or low time expenditure) if they can't make a reasonable living without it. The benefits that people receive do not make it worthwhile to not work, or to risk benefit fraud (since that's what you're essentially accusing them of here, alongside tax evasion). Utilise some common sense here, please.
How many high income households do you think are evading tax? Or is it just the 'lowly' of society? Nah, higher income households just think they're more intelligent about it hiding it offshore. Of course, your wee cleaner isn't going to have the sort of money to be having accounts outside of the UK, are they?
Of course your cleaner does. They're absolutely raking it in via tax dodging.
Have you thought about the reasons they refused your increase of hours? Do you know the ins and outs of all their personal circumstances? Do you know whether they have caring responsibilities, kids with extra needs, ill health/disabilities, was the extra hours you were offering enough to offset what they'd receive in benefit? You probably wont know all of this, because most of us don't divulge our personal lives to our employers.
Unfortunately though, that means people will make assumptions. The less nice of us, come to the worst ones.