How would taxation be an issue?
What I was meaning was that by taking on a child for 45 hours a week, you have time leftover which isn't being used.
For example, say your operating hours are 7.30am to 6.30pm - that's 11 hours a day, or put another way 55 hours a week.
Therefore you would have 10 hours during which you are not providing care for this child... so 10 hours you could sell to someone else, though realistically I'd say it would be unlikely that you would fill that left over time.
This is one reason why nurseries charge a daily rate, or session rate... if a child does less hours than the full day, the nursery still gets paid the full day rate.
One way to look at things... if say you operate 55 hours a week:
55 x £5.5 = £302.50
If you offer 45 x £5.5 = £247.50 you are already giving a discount of £55 a week.
That however may suit you fine as caring for a baby for 11 hours a day, 5 days a week isn't always that fun. Thus you may like them going home early some days.
Talk to the parent about what hours they are wanting... is it really 45 hours a week, or do they need to factor in additional time so that they can do drop-off, collection which fits around your school runs. No point in them dropping baby off at 8.30 if you left the home at 8.20 to do the school run.