Tony Blair was questioned by police last week

The letters also invite them to be re-interviewed as part of the inquiry headed by Metropolitan Police Assistant Commissioner John Yates.

The interviews are not expected to take place before Christmas.

About 90 people have been interviewed and three arrested but no-one has been charged. All involved deny wrongdoing.

'Formal means'

Mr Yates told MPs some weeks ago that there were "gaps" in the evidence provided by the political parties, including the government, and that "it would, of course, be regrettable from our perspective if we had to resort to any more formal means to gather this material".

BBC Political Editor Nick Robinson says that "formal means" refers to either arrest, a search warrant or charging an individual with perverting the course of justice.

He said it is not known who has received the latest letters but they are likely to include key members of the prime minister's staff such as his chief of staff, Jonathan Powell, head of government relations, Ruth Turner and head of political relations, John McTernan.

Arresting any of them or seeking a warrant to search Downing Street would be politically explosive and would risk being dubbed "disproportionate".

The inquiry began after it emerged earlier this year that a number of large secret loans had been made to the Labour Party before the 2005 General Election, and that some of those lenders had subsequently been nominated for peerages.

Timing of interviews

The investigation has since widened to cover the other main parties.

It is up to the people the police have written to decide on timings of interviews. Officers can only control the timing of an interview by arresting someone.

Scotland Yard is currently expected to hand over a file on the case to the Crown Prosecution Service in January. The CPS would then decide whether there should be any charges brought.