A panel of judges compiled a list of the country's 100 most influential females for Radio 4's Woman's Hour.
Further down were author JK Rowling at seventh and Scottish Deputy First Minister Nicola Sturgeon at 20th.
One judge, journalist Eve Pollard, said the list highlighted the sectors where women were still under-represented.
The Queen's granddaughter-in-law, the Duchess of Cambridge, did not make the list but the judges noted her potential to do so.
Ms Pollard said: "Most women on our list were judged to have power because they had reached a place where they have control - of policy, of direction, of influence, of staff.
"The panel, a democratic group, also felt that we should include some women who have what we describe as soft power - not hire and fire or innovative financial decisions but the ability to transform the way we think about ourselves.
"Inevitably, not everyone will agree with the 100 we have chosen. There are some omissions. For example, we had long debates about the Duchess of Cambridge. Is she influential? Hugely. Is she powerful? Not yet.
"What this list does is shine a light on those sectors where too few women are getting to the top, like politics, FTSE companies, the military and journalism.
"Our legacy, we hope, is that this list might change that."
David Cameron's speechwriter Clare Foges, singer Adele and broadcaster Clare Balding were among those outside the top 20 but on the full list.
The judging panel also included Conservative MP Priti Patel, Labour peer Oona King and crime novelist Val McDermid.
Figures compiled by the BBC News website last year showed fewer than a third of the UK's most influential jobs were held by women.
Women occupied on average 30.9% of the most senior positions across 11 key sectors analysed, including business, politics, the judiciary and policing.
Campaigners said progress was still too slow.
The top 20 names in the Woman's Hour list are:
More information about the Women's Hour Power List can be found here.
The Queen, Home Secretary Theresa May and Santander bank boss Ana Botin have been declared the UK's top three most powerful women in a BBC survey.