Britain's Olympic and Paralympic medallists capped a summer of sporting success as guests at a Buckingham Palace reception on Tuesday night.

About 225 athletes attended – and, for some, the event presented unexpected challenges. "I swear walking across that gravel should actually be an Olympic event," said swimming star Rebecca Adlington as she teetered across the palace quadrangle in high Kurt Geiger heels. "This is the last time when we all get together so it's quite sad.

Boxer Nicola Adams, whose nifty footwork helped power her to a historic gold, had been in training for the reception hosted by the Queen: "It was excellent. I was excited and nervous all at the same time. But I got my curtsey right so that was OK. I'd been practising"

On life after the games, Adams said: "I've been here there and everywhere. In a helicopter, in Rio with the prime minister and now I'm topping it all by meeting the Queen. "

The Duchess of Cambridge who, as an official ambassador for Team GB and ParalympicsGB ,was a regular spectator at British triumphs at London 2012, was among the royals attending.

"She said she had seen my first race in the velodrome," said cyclist Sarah Storey, who became the UK's most decorated female Paralympian this summer. "It was fantastic to chat to them and hear their experiences of our races." The reception was "the icing on the cake", she said.

Paralympic equestrian Lee Pearson provided the exclusive of the night with news that the duchess was taking riding lessons. "I had a right good chat to her. We were chatting about horses. She said she was learning to ride. I said 'if you ever want a dressage class, come up to Staffordshire'."

Team GB won 65 medals – 29 of them gold – while ParalympicsGB claimed 120, including 39 golds. Both came third in the medals tables.

The organising committee chairman, Lord Coe, who is expected to be confirmed as the new chairman of the British Olympic Association next month, said: "It is just another opportunity to say thank you for those extraordinary performances".

Earlier, Coe attended a cabinet meeting in Downing Street to urge ministers to help shore up the UK's Olympic legacy.

Ellie Simmonds, the Paralympian swimming gold medal winner, said she was already back in training. "I am really getting back into it," she said.

Peter Wilson, Team GB's shooting gold medallist, said: "If you had told me on 1 January 2012 that I would be an Olympic gold medallist and be meeting the Queen, I would say 'pinch me'. It's mega."

A British Olympic Association spokesman said: "In an extraordinary year that began with a celebration of the diamond jubilee, it is an honour for our Olympic and Paralympic medallists to be welcomed to Buckingham Palace by her majesty the Queen."

British Paralympic Association chief executive Tim Hollingsworth said: "Our medallists are honoured to attend today's royal reception and it constitutes another memorable occasion for those who helped to make 2012 a year in which Great Britain has been so hugely proud of the achievements of our Paralympic and Olympic athletes."

The reception was hosted by the Queen, who played her own part in the celebrations when she made her acting debut to become a Bond girl in a scene for the Olympics opening ceremony.

It will not be the last time at the palace for some of the guests. Britain's Olympians and Paralympians are to get their own honours list after prime minister David Cameron decided to place awards from the games outside the usual quotas.

A Buckingham Palace garden party next year will be held in honour of the athletes, Gamesmakers, volunteers and others who helped make the London games so successful.

In the palace's 18th Century Room, the Queen and Duke of Edinburgh met Cameron, Coe and other senior figures who made the Games possible.

Cameron said: "It was an amazing summer and I think people will cherish those memories, you know, almost more then the 1966 World Cup.

"I think people will look back and just think, what an incredible summer! Success after success, medal after medal and the whole country putting on its very best face for the world.

"What matters now is that we maximise the momentum and the legacy following the Olympics and Paralympics."

He said the meeting with Coe had discussed the physical legacy for east London, economic benefits and the sporting legacy. "There's also the legacy in terms of attitude to disabilities, which I think is a real chance of a step change in our country," he said.