The Compact Law organization gives a useful summary of the legislation on their web site
The Adoption and Children Act 2002

It really isn't a 'one size fits all'

In answer to the question

'Does an unmarried father have any rights to stop the adoption of his child ?'

The following reply is given -

'Yes, if he has a parental responsibility order or a parental responsibility agreement (see Children section). He can then apply to be joined as a party to the adoption proceedings.

If the father does not have a parental responsibility order or a parental responsibility agreement he still has some rights.

He will be asked for his consent, however, if he cannot be found his consent is not needed. Or if he does not consent the court has the power to override his refusal and still make an adoption order.

N.B.
In fact the adoption law was modified a few years ago to provide that an unmarried father CAN acquire parental responsibility for his natural child where he and the child's mother register the birth of their child together

* Please note it is still the responsibility of the COURT to overide the refusal of a natural father (where no such parental responsibility has ever been assumed) to adoption.