My apologies for the delay
The Judge does have the power to grant the adoption even if the father objects BUT only if Social Services (who will deal with this - not CAFCASS) believe that this would be in the best interests of the child
Social Services will indeed interview the father - and probably the grandparents and it is likely that they will be reluctant to end the biological bond unless it is absolutely clear that this would be better for the child
Whilst his lack of interest in the child is helpful none of the reasons you have given for the adoption are particularly convincing - and Social Services will in fact be concerned that she is not aware of his identity.
There is a risk that he will ask for contact - but given hillock on involvement and the potential risks you would be able to limit this to a local Contact Centre once a month.
However since it is likely that this will fall by the wayside very quickly it may well be that this will aid rather than hinder your case.
Your starting point is to approach your local Children's Services.
Be careful what you say to them as their approach is not the same as yours and you do not wish them to feel that you are simply "painting him out" of her life - which is what their suspicion will be
Please ask if you need further details