Does the father have joint parental responsibilities with you? Unless you were married to him, he will only have them if you have agreed to give them to him or jointly re-registered the birth after 1.12.03 or he has acquired them by Court order.
If he does not have parental responsibilities then I think you can appoint whoever you like to look after the child, but if you did die the father could challenge this in Court and try to get appointed as guardian or get a residence order, or an order giving him parental responsibility.
If he does have parental responsibility then I suspect he would be regarded automatically by the Courts as the person to have custody on your death, although they ought to take into account your wishes as expressed in your will.
I agree with Jenna - you ought to talk to him about this. You should also talk to the solicitor doing your will to see what can be suggested to maximise the likelihood of your wishes being carried out.