... so I'll try and rephrase it.
It is certainly possible to amend a previous year's return in this way and get a refund.
But it is also generally possible to include the expense in the current year's expenses. This is much easier and quicker both for you and for HMRC.
Also, you should be aware that each year HMRC select a certain number of people to inspect to check that everything is OK. Even if you have excellent records, being inspected is not much fun, apart from the worry that they may find a mistake you have missed there is the hassle of digging out all the records and providing them with the explanations they ask for - for instance with a childminder they may want to look carefully at what you have claimed for household expenses and there is bound to be an element of judgement, apportionment and approximation here which they may challenge.
Now they only inspect a tiny percentage of self-employed returns each year, and the way they select which ones to inspect is not made public (for obvious reasons), but it is generally assumed that as they are looking for people that may have made mistakes, if you have identified yourself as someone who has made a mistake in the past then you increase your chances of being selected.
sloggies I didn't mean to suggest that there was anything dodgy about your backdated claim, and now you have explained how it came about you did the right thing. But for general advice, and from the information the OP provided, inclusion in the current year is probably the way to go.