I agree with mouldycheesefan (not about the cheese tho!) that babysitters are not usually used for the type of thing you're thinking about.
Babysitters typically come when the children are getting ready for bed/in bed in the evening. It may be a naming/classification issue, but most people I know who have help during the day with their children call them nannies - even if they aren't trained nannies or are only providing a few hours of help. And there are lots of nanny agencies that will help such families find educated or multilingual nannies - plus tutor agencies of course.
I don't want to be negative but, having seen it before, I worry when a business wants to launch a completely new product or service, or when it has to re-educate the masses about what it does. Both those things can make it slower and more costly to start, and the business can fail before it gets going. My sense is that people pay very little for babysitting services (approx £8 per hour for one big babysitting agency in London vs £60 for 45 minutes I heard one tutor charging) and that it's hard to make money without big scale. Given that you will presumably have limited marketing funds to start with (like most startups), you'd want to be sure that this is a big problem, and that people will want to pay for it to be solved.
The other question to ask is, if this is a big and lucrative market, why haven't the big nanny/babysitting firms moved to fill that gap? Or how are they filling that gap for their clients - are they calling it something different perhaps?
So I'm back to my original point - more research! It's the best thing to do that this stage and it's completely free (I use SurveyMonkey). I'd ask people (as many as possible) what issue they have around childcare/babysitting/nannying that needs to be solved, and see if your idea is one that many people have. If they do, then you can explore more - how much would they pay to have it solved, how often, what type of people exactly, how many clients/placements would that give you in a year. Then you can start to build a business case to see if it will work for you.
I'm all about the research so it helps you hone your idea quickly and do a business viability assessment before you've spent your first £. Hopefully it will prove that there is a market (and fair price) for your product and then you'll be off and racing!