The UK does still need a navy. We are an island nation and most of our trade comes in by sea. So there is a requirement for a surface/sub surface fleet to ensure the sea lanes to this country remain open. The ships/subs have a much better loiter time than aircraft can provide one that can be measured in days and weeks not hours.
secondly we still have protectorates across the world that we as a nation are responsile for their defence and support in times of national crisis hence the Guardships carry disaster relief modules
thirdly our economic zone in the waters round this island require patroling to enforce international law and to protect our interests.
forthly we still have a merchant fleet who require protection and escort at times across the worlds oceans this also includes ships registered in some of our protectorates.
Lastly the Navy helps keep unemployment figures down.
Yes the RAF does help with some of the above tasks but Navy ships tend to be able to stay on station alot longer.