Mrs Nelson's husband, Paul, demanded the move after an official report criticised the way police had investigated death threats to the lawyer before her killing. The Independent Commission on Police Complaints found officers investigating the threats to be "hostile, evasive and disinterested".
But Lord Dubs, a Northern Ireland Office minister, said the RUC was best qualified for the murder hunt, which is headed by David Phillips, Chief Constable of Kent.
Mrs Nelson, who had three children and represented many prominent nationalists, died when dissident loyalists blew up her car in her home town of Lurgan, Co Armagh, last week.
Mr Nelson, the SDLP and Sinn Fein have all called for an independent inquiry. Many solicitors and several human rights organisations are supporting the demand.
The RUC Chief Constable, Sir Ronnie Flanagan, defended his officers, saying they were innocent until proved guilty.Reuse content