mary I am unclear from your posts about whether you have other children in your household other than your 12-year-old DSD. If you don't, I will forgive you for not having a realistic picture about childcare.
For a woman with a 9-5 mon-fri job (like me), I have worked out that it costs about £55,000 in childcare from the time until the age where that child no longer needs any form of day care (£110,000 in my case because I have twins). Obviously the bigger costs accrue in the early years, but even for a single primary-school-aged child you are talking about £4000 per year to cover wraparound care and holidays. This is simply prohibitive for a lot of people on ordinary salaries (let's remember that the average full-time salary in this country is about £25,000 p.a. gross), whether they are single parents or married or LPs. LPs may have more help with costs through WTC but they don't have a partner who can pull up the slack for childcare.
The figure that lone parents can claim toward childcare is up to 70%. This applies only at NMW level and is cut as soon as you start earning more. You only start coming out on top again once you earn more than £30,000 (so that will be about 25% of the population only then).
I earn twice NMW and after paying childcare I am left with less than someone on benefits. In my case I consider it worth it but if a NMW earner is losing out both financially and on time with their child, is it? Is the child winning if they see less of their parent and have less money available?
Of course, if you happen to have one of these NMW that operates shifts patterns or weekends, you're unlikely to be able to find childcare that will fit anyway. Most LPs I know who work are relying massively on family help to carry out childcare, partly because they cannot find appropriate childcare and partly because they couldn't afford it even if they did.