A silver medal for Heather Frederiksen in the pool had taken the GB tally to 103 medals - one more than the haul from the team in Beijing with three days of competition still remaining - before Cockroft's triumph.
Liz Nicholl, chief executive of UK Sport, said: "To win at least 103 medals is a fantastic achievement particularly when you consider Paralympic sport is becoming hugely competitive with more nations investing significant resources in success."
ParalympicsGB chef de mission Craig Hunter said: "It is testament to the talent, dedication and skill of the athletes who make up the team as well as to their support staff and to the funding we receive from the National Lottery and commercial partners."
But he added: "The final target remains to finish second overall in the medal table. We know that this will be a close-run thing with three more days to go."
Cockroft took the overall medal tally to 104 at the Olympic Stadium to signal the start of a successful evening on the track for Britain.
The 20-year-old Halifax racer, the world record holder and the 100m champion, finished in 31.90 seconds, more than two seconds clear of the field.
Six-time London Marathon winner Weir, 33, then took 800m gold in a nail-biting race to further extend ParalympicsGB's medal haul.
"That was hard work," he said. "I just had to dig deep."
Arguably the moment of the Games came when teenage world record holder Peacock, who lost his right leg below the knee after contracting meningococcal septicaemia at the age of five, destroyed a 100m field that also included South African Pistorius - the face of the Games.
Pistorius said: "We witnessed one of the great Paralympic performances. He's still young. He's got a great future ahead of him."
Peacock said: "We have had a great day. Hannah opened up the evening with a gold straight away and I knew David was going to win. It was just unreal."
Earlier, Storey, 34, won her fourth gold of the Games when she crossed the line more than seven minutes ahead of her rivals.
The all-time British record belongs to Mike Kenny, who won 16 golds in the four games up until 1988 - which predates the modern Paralympics.
Storey attacked almost from the gun at Brands Hatch and increased her lead throughout the race, with no other rider able to match her.
She told BBC Radio 5 live: "The records are lovely things to talk about but each race is an achievement, each is hard fought. Just being able to say that you have won for your country is a great honour."
In the pool, Craig set a new world record as he took gold for Great Britain in the men's S7 400m freestyle.
The teenager said: "I wanted to start [my career] in Rio , but I now want to go there and smash that [world record] again."
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