With luck the nannies who apply will already have a CRB check done in the last 3 years, as if they have registered with an agency then the agency will have done one... if they are Ofsted Registered, then Ofsted will have done one. Ofsted are not updating CRB checks... thus the date of the check will be when they initially registered with Ofsted. A new system is coming in, called the ISA, thus Ofsted are not renewing CRB checks on an annual basis (like the previous Childcare Approval Scheme).
As long as someone has had a CRB check in the past, then just take a look at that (especially the back of it, where minor offences are listed) that will give you some reassurance that at the time that check was done, the person was not known to the police.
Try to tune into your Gut feelings... trust your gut feeling... is this person someone you like, someone you would avoid? We make that sort of judgement everyday walking down the street... you know when you see someone and think, oh I don't like them but you can't think of a rational reason why.
In my view you are unlikely to be able to check ALL references. Take a nanny like me, I have childcare references dating back 20 years. Would you really check a reference that is 20 years old? What are the chances that the contact details for that reference are wrong? Highly likely to be wrong in my view.
So aim to verbally check references over the last few years... you may be able to get back as far as 5 years. Written references dating back further will give you a general feel for the person and the verbal references will with luck backup that feeling.
Chat to parents about the nanny - their personality, what they are like as a person, what they liked doing with the children, places they went with the children, how the parents felt about the nanny driving a car, if they were looking for another nanny would they consider that nanny again, if not why not? The reasons why not may help you know what limitations there could be - such as the nanny may not be great with school aged children, but wonderful with babies/toddlers/pre-school.
See how your own children react to the nanny. See how the nanny reacts to your children... how much interaction there is. If the nanny sits on a chair the entire time... it's a non starter in my view. Nannies in my view will quickly be on the floor with young children interacting at the child's level.