Yes you can claim a portion of your mortgage interest.
navyeyelasH, don't be so shy - yours is the best answer here!
Unfortunately there is no hard and fast rule - HMRC's own internal guidance (linked to earlier in the thread) says "The following examples are a guide only and intended to demonstrate the principles to be applied. The examples are not intended to be prescriptive; each case will be dependant on the facts."
So in principle HMRC agree that if you use part of your home exclusively for your business (whether that business is childminding or anything else) for part of the day, you can claim part of any of the revenue costs that you incur in making that part of your home available. Interest is a revenue cost, so you can claim part of it. Any capital repayment part of your mortgage is not a revenue cost so you cannot claim that.
But what proportion you can claim depends on the individual circumstances, no one formula fits all. It is up to you to come up with a calculation and a convincing argument to back it up. HMRC might query your tax return and ask you about your explanation, but they probably won't unless you are claiming a large amount of expenses in relation to your income.
Where an accountant is useful is in coming up with a calculation and an argument that he knows will convince HMRC, but there is no reason why you shouldn't try it yourself - it is very unlikely that you would be penalised for claiming too much interest as long as your calculations are correct and made in good faith, so all you have to lose is the potential tax saving from a more agressive calculation. Base your calculations on the HMRC examples (I'll give you the link again here) and you will have a head start in any discussion!
Finally, in order that you do not have a potential CGT problem, you should make sure that any part of your home that you do use for business is also used for non-business purposes. If you have a home office, it is likely that you will do your domestic paperwork in there too. If you have a playroom that is used by mindees during the week, your own children/neices/whatever are likely to use it at the weekend (so you would only claim 5/7 of the cost, or if they use it in the evenings too some calculation on an hourly basis).
Accountants in the know about this sort of thing often follow messages on the freelancers topic.