It can be done and you do need the natural fathers permission. If you can't find the natural father, you will need to show proof that you have at least attempted to locate him (i.e. adverts in local papers, contact his family to see where he is etc.) You can do this either through a private social worker who specialises in adoptions (expensive) or you can go to a government Social Worker (very slow due to workloads), alternatively, you can approach the family court (at any magistrates court) and start your application there.

You will need to convince the magistrate that the adoption is for the right reasons and need to prove to the social worker that this will be in the best interests of the child. The natural father can refuse permission, in which case the magistrate will then be left to make a decision based on all the factors involved.

The process will be all about your fiance as he will be the one applying, so you will personally not have that much input in things, although you will both be required to undergo interviews with the SW. The children will also be asked how they feel about this, but their ages at the moment are quite young to hold much sway. There will also be additional costs, as the children will require assessment(s) by a qualified child psychologist and your fiance may also have to be assessed.

If the natural father hhasn't been on the scene for a considerable amount of time, if at all, and he has not supported the children then you may be in for a good chance, especially if you have been in the relationship together for a good many years. The fact that you are not yet married may hinder your application somewhat, so you will need to prove (as above) stability and responsibility.