How does an ex-spy link BP, Libya and Lockerbie bomber? Who Knows Who investigates the key players at the heart of a growing transatlantic rift - from deals in the desert to the boardroom, via MI6.

Tony Blair shakes hands with Colonel Gaddafi. (Getty)

The only man convicted in connection with the 1988 Lockerbie plane bombing over Scotland, Abdelbaset Ali Mohmed al-Megrahi, was released in 2009 on compassionate grounds. He is terminally ill with prostate cancer.

He returned home, personally escorted by Saif Gaddafi, son of Libya's leader Colonel Gaddafi, to a hero's welcome in August 2009.

The celebrations sparked fury around the world and were condemned by President Obama and then prime minister Gordon Brown. Nearly a year on, al-Megrahi is still alive in Libya and his name is back in global headlines.

Rivals, white knights and Libya: who wants BP?

Thousands of miles away in the US, a group of senators has called for an inquiry into an admission by British energy giant BP that it lobbied UK ministers to get them to speed up the signing of a prisoner transfer agreement, in order to rescue an oil deal with Libya. BP insists it never lobbied about Mr al-Megrahi personally.

The witnesses the US politicians call could include Scotland's Justice Secretary Kenny MacAskill, former justice secretary Jack Straw, Lord Browne, the former BP chief executive, and Tony Blair.

So who sped up the process which may have led to al-Megrahi's release? What did Tony Blair agree at the "deal in the desert"? And what is the BP connection?

Shortly after al-Megrahi's return home, Britain's former "man in Tripoli" Sir Oliver Miles told Channel 4 News he believed a deal had been done between the UK and Libya, to get al-Megrahi to drop an appeal against his conviction.

The former UK ambassador to Libya said: "I think Tony Blair originally thought that he could deal with it quite simply by [sending] al-Megrahi back to Libya under the prisoner transfer agreement. It turned out it wasn't as simple as that."

One man who knows more than most about what took place is Sir Nigel Sheinwald - Britain's ambassador to the US since 2007. Once Blair's right-hand man, he has been at David Cameron's side throughout the new prime minister's first official US trip.

Sir Nigel previously served as an adviser on foreign policy to Blair. Libyan ministers and diplomats are said to refer to the "Nigel and Tony" double act.

In 2003, with US approval, he chaired the secret meetings in London with the Libyans that led to an easing of international relations with Colonel Gaddafi.

Intriguingly, Mr Cameron's coalition partner also has a connection to Gaddafi. Before entering parliament, Deputy PM Nick Clegg worked for a lobby firm called GJW. One of its clients was Libya and a key project is said to have been "improving the reputation" of its controversial leader.

Sir Nigel Sheinwald was at the heart of this rehabilitation of Libya in the eyes of the West. He was sitting next to Tony Blair at the now infamous meeting in Gaddafi's tent in 2004.

Tony Blair shakes hands with Colonel Gaddafi. (Getty)

Sir Nigel was again at Blair's side in 2007 when a prisoner transfer agreement was struck. On the same day Blair looked on as BP boss Tony Hayward signed a provisional agreement over $900m gas and oil exploration rights in Libya. Both deals later stalled and al-Megrahi's ill-health was the official reason for his release.

Another key player, and a name which should interest the US senators, is Sir Mark Allen. He was in charge of the Middle East and Africa department at MI6 until he left in 2004 to become an adviser to BP.

It is known Sir Mark lobbied then justice secretary Jack Straw to speed up an agreement over prisoner transfers to avoid jeopardising a major trade deal with Libya.

He made two phone calls to Mr Straw - who later let slip Sir Mark's involvement to a select committee. He said: "I knew Sir Mark from my time at the Foreign Office - he has an extensive knowledge of Libya and the Middle East and I thought he was worth listening to."

Sir Mark, an Oxford graduate and a fan of falconry, has been credited with helping to persuade the Libyans to abandon development of weapons of mass destruction in 2003. He is said to have "charmed" Gaddafi out of his international isolation.

But has BP's influence been overplayed? Sir Oliver Miles, the former British ambassador, believes so. He says that the US senators, angry at the Gulf of Mexico oil spill disaster, are trying to "kick BP while it's down".

He said that Libya had signed deals not just with BP, but also with Shell and ExxonMobil - the three biggest energy firms in the world.

Speaking to Channel 4 News he added: "Libya knows the only way it can achieve a boost in oil production is by bringing in the world's biggest oil companies.

"You don't have to look for any dirty business to explain why they're doing business with BP."

Pan Am flight 103 crashed in the Scottish town of Lockerbie in December 1988 when a bomb exploded on board. A total of 270 people died - 243 passengers, 16 crew and 11 people on the ground. It is the worst terrorist atrocity in British history.