A British man arrested over the murder of his American wife and baby daughter will be returned to the United States within "a matter of days" to face the allegations.

Neil Entwistle (27) agreed to be sent to the US "as soon as possible" when he appeared before Bow Street Magistrates' Court in central London this morning.

The unemployed computer programmer, who was arrested in the capital on Thursday, is accused of shooting his wife, Rachel, in the head before turning the handgun on nine-month-old Lillian at their home in Massachusetts three weeks ago.

At yesterday's court hearing, Entwistle signed a form to waive his right to extradition proceedings.

He was told his decision was irrevocable once he had signed the appropriate form.

As he filled out the paperwork, he caught a glimpse of his father, Cliff Entwistle, seated behind him, and smiled briefly.

District judge Anthony Evans had asked him: "You are agreeing to be sent immediately to the US and there will be no extradition proceedings?"

Entwistle, clad in grey tracksuit bottoms and a black sweatshirt and flanked by security guards, nodded and replied: "That's right, yes."

There was no application for bail and Mr Evans said: "I remand you in custody pending your removal to the United States."

A relaxed-looking Entwistle left the court smiling at his legal team.

When he made his first appearance at Bow Street last night for the start of the process, he had indicated he would not consent to extradition "at this stage".

However, after this morning's brief hearing, his solicitor, Judith Seddon, denied that he had changed his mind, insisting it was always likely he would consent to return to the US.

He was anxious not to add to the distress of his wife's family or his own, she said.

"Neil Entwistle has today consented to his extradition to the USA to face the allegations made against him," Ms Seddon said.

"He has consented at the earliest opportunity because he wants to co-operate with the authorities in any way that he can.

"He is anxious that a delay might cause his wife's family and his own additional distress, something he wants to avoid.

"He believes he will receive a fair and proper hearing in the US on these very serious allegations."

He could be returned to the US "within the next week" or in "a matter of days", she said.

Asked whether he denied the allegations, Ms Seddon declined to comment further.

Entwistle will be sent to the US once Home Secretary Charles Clarke has formally approved his return.

This could happen as early as today or possibly early next week. Once approval has been given, Entwistle is likely to be put on a flight within 24 to 48 hours.

Asked about the details of the arrangements for his return, the Home Office said it could not discuss individual cases.

The heartbroken family of Rachel and Lillian said they were "deeply saddened" and shocked by his arrest over the killings.

Family spokesman Joe Flaherty said it was "incomprehensible" how Rachel and baby Lillian's love and trust of Neil Entwistle could have been "betrayed in the ultimate act of violence".

"Rachel and Lily loved Neil very much," Mr Flaherty told reporters at a news conference in Massachusetts.

"Neil was a trusted husband and father and it is incomprehensible how that love and trust was betrayed in the ultimate act of violence.

"We are heartbroken at the loss to understand how this happened."

Entwistle left the US to stay with his parents in Worksop, Nottinghamshire, a day after the killings and the day before the bodies were found.

Earlier, Middlesex District Attorney Martha Coakley told journalists in the US he had been having financial problems before the murders and had no apparent income to support his family.

She said a reporter's suggestion at the press conference in Cambridge, Massachusetts, that Entwistle was a "desperate man" was "not an unfair conclusion".

He has been linked in reports to a website offering what appeared to be get-rich-quick pyramid schemes.

As well as two counts of murder, the 27-year-old also faces accusations of illegal possession of a firearm and illegal possession of ammunition.

Ms Coakley said investigators believed Entwistle had carried out the murders with a gun he had taken from his father-in-law's collection and later returned secretly.

Forensic evidence linked it to both Entwistle and his wife but she had never used it, she said.

Detectives believe the mother and baby were murdered on the morning of Friday January 20, and that Entwistle took a BA flight to London from Boston's Logan International Airport at 8.15am on the Saturday.

He had managed to buy a ticket on the phone at 5am using a credit card.

The bodies were discovered by police on Sunday evening, hidden from view by piles of fluffy blankets and duvets.

Explaining what investigators believed had happened, Ms Coakley said: "Some time on Friday morning, Neil Entwistle, with a firearm that we believe he had secured at some time before that from his father-in-law, Joseph Matterazzo, shot Rachel Entwistle in the head and then proceeded to shoot baby Lillian, who was lying on the bed next to her mother.

"We believe possibly that this was intended to be a murder-suicide, but we cannot confirm that."

She added: "What we believe happened next was that Neil Entwistle returned the gun to his father-in-law's home in Carver, that he then made preparations to leave the country."

Entwistle was arrested at Royal Oak Tube station in west London shortly before noon on Thursday "without incident" after a provisional extradition request from the US was received by British police.

Such requests are issued in "circumstances of urgency" and must then be certified within 60 days before full proceedings can begin.

Until then, he had only been named as a "person of interest" in the investigation.