It's a lose-lose situation for an NHS consultant. If they sterilise someone who may enter another married-type relationship and want children - problem. If they sterilise someone who has a child under five, the age group most likely to die (huge apologies, but this is factually the case) - again, problems if and when the bereaved parents decide to try again. Yes, you can get almost anythingdone privately, but will undoubtedly be required to sign disclaimers re. change of mind or personal circumstances.
BTW My info is that consultants round here recommend you wait till youngest child is 5 - they don't go on age of adult but will suggest counselling in a 'less mature' bloke.