Failure to comply could result in him being returned to prison, two years after he last walked free from an eight-week sentence for breaching a financial reporting order designed to recover some of the family's estimated £200 million fortune.
In April, Adams' younger brothers Tommy and Michael were also arrested as part of Operation Octopod, a specialist police investigation designed to target the family's assets, as well as those of other criminal clans in Britain. The brothers are waiting to find out if they will be charged.
Despite their fearsome reputation -- one underworld figure once said "they make the Kray brothers look like clowns" -- members of the Adams family have long evaded justice. Linked to at least 25 murders, torture, violent extortion rackets, drug dealing and the £26 million Brink's-MAT armed robbery (which involved three tonnes of gold bullion), the family were known as the A-Team and the Clerkenwell Crime Syndicate through the 1980s and 1990s.
Terry is the eldest of 11 children born to Irish Catholic parents in Islington, north London, in the 1950s and 1960s. He turned to crime as a teenager, starting with petty theft, then moving into extorting market stallholders in north London with his brothers, and graduating to armed robbery. He was seen as the brains of the family, while Tommy became the financier and Patrick -- known as Patsy -- developed a reputation as the violent enforcer.
Patsy now lives on the Costa del Sol in Spain and has so far avoided the latest round of arrests. Tommy has been jailed for drug dealing, and was convicted but later cleared of helping launder proceeds from the Brink's-MAT haul. Other siblings have not been connected with the crimes of their brothers.
During their heyday they were believed to have had police officers, prosecutors and lawyers on their payroll. The gang was linked to the shooting of the Krays' notorious chief henchman, Mad Frankie Fraser. Another former A-Team associate is rumoured to be encased in concrete beneath the O2 Arena for failing to stay loyal, while a crooked financier who fell foul of the family was tortured to the point where his nose and ear were supposedly left hanging by a sliver of skin.
The Adamses apparently began to franchise out the family name, charging gangsters on the make for association with the clan. They are believed to have joined up with Colombian drug cartels. Terry and Ruth's £2 million home in upmarket Finchley had rooms filled with expensive art.
"The Adamses are probably the last of the old-school British crime families," says Wensley Clarkson, author of a book on Britain's gangs. "They wanted to be accepted into the Establishment. They're a bit like the Sopranos - they made their money and then sent their children to private schools, bought art, invested in legal businesses."
By the beginning of the century, the brothers had accumulated enough money to go into legitimate businesses, including restaurants, nightclubs and even a failed attempt to buy Tottenham Hotspur Football Club. It took until 2007, when he was convicted of money laundering, before Terry Adams was finally behind bars, sentenced to seven years. He was out by 2010, collected from jail in a Porsche accompanied by two burly minders. The ever-loving Ruth treated him to a "post-prison makeover" at a luxury spa, including a revolutionary stem-cell facelift, which landed him back in prison for breaching the £500-per-item limit he was supposed to be confined to as part of a Proceeds of Crime Act order.
Ruth Adams is the sole shareholder and chief executive of N1 Angel, an online menswear company that employs Terry as creative designer and is frequented by premiership footballers who snap up its £800 suits and frock coats.
The couple say that the house in Finchley, the works of art and the designer lifestyle are long gone; they now live in a one-bedroom apartment in London Colney, near St Albans.
Clarkson believes old crime clans like the Krays and the Adamses are a thing of the past. "Those families may have been brutal but the current situation is far more sinister -- you have the Eastern European gangs like the Albanians and Russians, who are so cold-blooded, so violent, and the police don't even know who they are."