I'm surprised that the council are actually your employers. To do the job in Ipswich you have to apply to an agency in the Republic of Ireland!
If you've got any paperwork relating to your state pension, your NI number should be on there. It might not actually say 'National Insurance Number'. It could be given as something like 'DWP Reference No.". If you can find something that's made up of two letters, six digits and one letter (For example, "AB123456C" or "AB 12 34 56 C"), that will be what you're looking for.
Chris