If you are able to access ancestry.co.uk they have GRO births transcribed up to 2005.
Some years ago I transcribed for a FreeBMD 'syndicate'. The process was rigourous and thoughtful and gave me confidence that the project would produce accurate results.
Though they may not have finished transcribing the years you want they do appear to have the images on the site. Go to the main page and click View Images. You then have to narrow your search down to Births/Year/Quarter/1st letter of surname which brings you to a list of pages. You have to guess where in the list the surname you want will be found and move up or down depending on what you find.