The online searchable birth index goes up to 2005, the search method would be the same as any birth record but as it's a post 1911 event the maiden name of the mother will be given in the index along with district, volume and page details.
Where you might come unstuck is if the child was born out of wedlock and therefore registered in the surname of the mother, without knowing the surname to search for you don't really have a record to trace.