You need to start by looking for likely births with your grandad's surname (assuming the child was given his name??) in the right area at the right time ............. do you have any names and dates to go on? Happy to search birth records for you, but if it's a Smith or Jones in London, for example, you're going to struggle. The child may have taken his mum's surname which I assume you don't have? You can email me details at
[email protected] if you prefer not to put them on here.