The Queen and Margaret Thatcher disliked each other with the monarch mocking the former prime minster's "1950's Royal Shakespearean accent", a new book has claimed.

Queen Elizabeth apparently did not get on with the Iron Lady socially and mocked her accent, which she said was akin to a thespian's portrayal of the Bard.

In his The Queen and Mrs Thatcher: An Inconvenient Relationship, author Dean Palmer says the pair disagreed on a wide range of issues including foreign policy and the miners' strike.

"For over a decade they quietly waged war against each other on both a personal and political stage, disagreeing on key issues including sanctions against South Africa, the miners' strike and allowing US planes to bomb Libya using British military bases," he wrote.

The Queen disapproved of Thatcher's "love to lecture" during the pair's weekly meeting at Buckingham Palace and their relationship reached its nadir during the Falklands war, Palmer claims.

The monarch resented Thatcher's image as "mother of the nation" and that her prime minister received the salute on British troops' homecoming parade and not her.

Their relationship plummeted to the point where the Queen would refer to Thatcher as "that woman" in front of Commonwealth leaders and rebuffed suggestions the pair should co-ordinate matching outfits.

Palmer writes they only became more cordial after Thatcher left office after 12 years as premier at Number 10, evidence of which came when the Queen attended Thatcher's funeral in April 2013.

Buckingham Palace refused to comment.