I'm afraid you're going to have to go down the route that all of us doing our family trees are, that is by starting at the facts you know and working backwards by ordering certificates. I have had a look at Jean Prestons whose birth was registered in the quarters ending March and June 1936 (you can't look up a specific day or even month, and it's not by when they were born but by when the event was registered). There are quite a few! There was
Jean Preston born Salford to a mothers whose maiden name was Ellams
Jeane L born Liverpool S maiden name Steinberg
Jean born in Barnsley maiden name Denton
Jean born in N Brierley maiden name Goodieson
Jean I Born Fyle maiden name Reynolds.
Are any of these your mother? (I'm guessing the first one). If so then I have found the marriage (registered in the quarter ending September 1935, which means that they could have married in the July, August or September of that year) of William Preston and Hannah Ellams in Salford. Your best bet (if this is your Grandparents) is to order this certificate from Salford Registry Office, details here
http://www.salford.gov.uk/living/bmd/copycert. htm
Once you have the certificate in your hands you will know the ages of your Grandparents when they married and also the names of their fathers. You can then look for the birth certificate of your Grandmother which will give the names of both her parents and the maiden name of her mother. If you wish you could then order the marriage certificate of her parents. If you get back as far as 1901 you can find the family on the census.
Good luck. Any further questions are best posted in History under the Genealogy heading.