To check an NI number

Call the Inland Revenue National Insurance Enquiry line on +44/0 845 7413355 press 9 for touch-tone phone and then 4 for all other enquiries. You'll need to provide the operator full name (inc. any middle/very first names), date of birth, and address.

Other menu options

1. replacing lost, stolen, or damaged numbers
2. are a new employer
3. need forms or leaflets
4. (the rest)

There's some more info from an employer perspective, National Insurance Number Information For Employers from the Inland Revenue National Insurance Contributions FAQ. Oddly, it doesn't list the phone number above.