Some childcare is easy to find, others less so:
Nurseries, childminders, nannies for regular care can all be found relatively easily using a combination of local recommendations, Ofsted reports, viewing/meeting and established agencies.
Emergency ad-hoc childcare is a bit trickier but there is at least one agency set up specifically for that already. Most parents are able to take the odd ad hoc day off work too.
Before/after school care and holiday care is trickier. There is often a rush for a handful of BC/ASC or suitable CM places. I know many parents who have found it stressful and end up with something unsatisfactory. Holiday clubs are often few and far between, not local or not full days.
There are very few agencies that deal specifically in providing qualified, experienced and suitable childcare in this area.
As for babysitters, I'm one of those parents who has used a sitter I've never met before through an agency. I know quite a few parents who have. (Many of us just didn't go out as a couple for the first 2 years but eventually decided that wasn't much of a relationship).
None of us have family nearby, many of us use nurseries who prohibit their staff from babysitting (this seems to be becoming a thing now in London...) or CMs that aren't willing to do evenings/weekends. The only friends I know who use their nanny to babysit don't live locally so sharing childcare isn't feasible.
The only local recommendations for babysitters I've had have been for young au pairs or teenage daughters. I preferred to leave my 2 yr old with a very experienced ex-nanny in her 40s instead (who has turned out to be lovely and is now a regular). Once dd is older I'll probably be more willing to use someone less experienced but only if I know the parents/employers.
Unless you're going to offer something more than Sitters though, there doesn't seem to be much of a gap in that market for babysitting.
If you nail after school/school holiday care though you'll be inundated.