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 nine-year-old's family sought redress from NHS England and South Central Ambulance Service after he became unwell in 2007 aged six weeks.
He received treatment at the Royal Berkshire Hospital, but it came too late to prevent injury to his brain.
The organisations denied liability, but agreed to settle the case.
The High Court heard that the child, who is from Berkshire but who cannot be identified, requires around-the-clock care.
He has severe cerebral palsy, profound learning disabilities, deafness, severe visual impairment and epilepsy.
His legal team alleged his condition was the result of negligence by two GPs and a paramedic.
They argued the boy would not have suffered the injuries if he had been given antibiotics and hospital treatment sooner.
Mr Justice Kerr said the payout, which will be used to provide the boy with life-long care, "marks the end of a long and difficult process".
He will receive a £2.3m lump sum and index-linked annual payments of £237,660 which will increase to £259,257 when he turns 19.
Speaking after the hearing, the family's solicitor, Olivia Scates, described the case as "extremely tragic and distressing".
"His family have been devastated," she said.
"I am delighted the family will now have access to the help they need to provide for his extremely severe disabilities."

Shanghai have signed the Argentina forward, 32, from Boca Juniors but no details were given over the contract.
Shanghai, coached by ex-Brighton boss Gus Poyet, are reported to have agreed a deal worth £40m for Tevez including a salary in excess of £310,000 a week.
Boca Juniors said: "Good luck Carlitos. You will always be in our hearts."
Tevez played for seven years in the Premier League and won the title with both Manchester clubs.
He also lifted the Champions League trophy with United in 2008 before joining Juventus in 2013, where he won two Italian championships.
On 23 December Chelsea agreed terms with Shanghai SIPG for Brazil midfielder Oscar, 25, in a move that is estimated to cost £60m.
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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.
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A boy who suffered "catastrophic brain damage" after contracting meningitis as a baby is to receive £4.6m in compensation from the NHS.
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Ex-Manchester City and United striker Carlos Tevez has signed for Chinese Super League side Shanghai Shenhua, the club confirmed on Thursday.