Police searched the home of Mr Socrates's uncle this week in connection with the affair, which is said to have taken place when Mr Socrates was environment minister in a previous socialist government. Britain's Serious Fraud Office is said to be investigating the unexplained transfer of some 4m euros to bank accounts in Portugal at the time of the deal, press reports say.
Mr Socrates is alleged to have waived environmental restrictions in 2002, following intervention by his uncle and cousin, to grant the British company Freeport a licence to build the Alcochete mall or "village outlet", a gigantic emporium of designer shops south of the Portuguese capital.
The English royal family is reported to have a large stake in Freeport, which was taken over by the US conglomerate Carlyle in 2007.
Mr Socrates denies having misused his ministerial position to allow the shopping mall to go ahead, or having taken bribes from Freeport. In a rare television appearance at the weekend, he scorned the storm of media allegations, which was spearheaded by Lisbon weekly "Sol".
"The reports and the way they are presented are meant to target me personally and weaken me politically in an election year," Mr Socrates said. "Those who think they can beat me this way are wrong, because I'll fight to defend my honour, my integrity."
The Alcochete project was one of a number of major schemes that carved through Portugal's virgin lands, sometimes in defiance of environmental protection orders, in a drive to modernise the country.
The scandal has re-emerged at the worst possible moment for Mr Socrates, who faces general elections this autumn battered by the economic and financial crisis sweeping Portugal.
Environmental approval of the Freeport Outlet project met all legal requirements at the time, Mr Socrates said. He denied that the go-ahead, granted three days before general elections in 2002, was given with "unusual haste". The shopping complex, built in an environmental protection area along the Tagus estuary, needed cabinet approval for regulatory changes.
Ministers reportedly approved the changes just three days before the polls, which Antonio Guterres's Socialists lost to Jose Manuel Durao Barroso's conservative Social Democratic Party. Portugal's environment secretariat subsequently granted planning permission.
"I never gave any instructions to give the case urgent treatment," Mr Socrates insisted. "I reject all insinuations and slanderous allegations that involve my name regarding this case."
The media spotlight focuses on the prime minister's uncle and cousin, Julio and Hugo Monteiro. Hugo Monteiro is alleged to have held meetings with Charles Smith, a Scottish intermediary contracted by Freeport to ease the deal. Julio Monteiro is then said to have used his kinship with Mr Socrates to set up a meeting with the erstwhile environment minister for Mr Smith.
Mr Socrates vaguely recalls meeting Mr Smith in 2001, but "only to present to him the government's environmental requirements," after his ministry had twice blocked the building project. He says he has nothing to do with his uncle's business operations.