might not be so straight forward, if he is named on the birth cert.
a problem with that if the embassy find the father or member of his family and if the embassy realise this is not true, tell a lie then wave your visa goodbye.. trying to obtain a visa by deception.. i'm not saying this would happen, but you have to realise the worse case scenario and the results of your actions.
if he is named on the birth cert, can you not buy the father off and get him to write a letter stating he wishes his son to join his mother and live in the uk ? is your g/f on talking terms with him ?