Their inquiries will focus on an apparent three-hour discrepancy between the time of death as stated by her husband, Lord Caithness, and times given during the inquest in January.
Although the case is not being reopened, police will have the power to re-interview witnesses and check on details not heard at the inquest.
Lord Caithness told the inquest that his wife, Diana, had gone upstairs at 6.20pm on 8 January while he and their 15-year-old daughter were playing cards. About 10 minutes later, Lord Caithness said, he heard a 'dreadful noise'. He then found his wife's body.
However, the doctor who was called to their Oxfordshire mansion, Dr John Groves, said that his examination estimated death at some three hours earlier. A neighbour, Jane Lambert, also said that she heard a loud noise coming from the Caithness home at about 3pm.
Lady Caithness was said to be distressed after she had learned of her husband's relationship with Jan Fitzalan-Howard, a secretarial employee of the Princess Royal and Princess Michael of Kent. The former transport minister quit his pounds 45,000 a year job within hours of his wife's death.
The inquest found that Lady Caithness had killed herself with a double-barrelled shotgun. A formal suicide verdict was recorded. Since then, Lady Caithness's parents, Major Richard Coke and his wife, Molly, have lobbied hard to have the evidence re-examined.
Detective Chief Superintendent Tom Morrison, head of Thames Valley CID, said that due to 'some concerns' raised by the family of Lady Caithness, there would be a review of the case. This would concentrate on 'issues' that did not come out at the inquest, he said in a statement.Reuse content