neddyw you need to go to the record office rather than the library, The Record Office is in Marshall Street not far from Piccadilly, you'll neede a readers ticket so take 2 forms of id that include your name and address, you are issued with a readers ticket that last a few years, you can only use pencils and no erasers are allowed,
you can check the catalogue here:
http://www.gmcro.co.uk/
The Manchester and Lancashire Family History Society library and research centre is in Piccadilly and easy to get to, they have restricted opening and you would need to take an annual membership (£15 per year) but it is a great library and will help you tremendously.
http://www.mlfhs.org.uk/