Halsted is now ranked 15 in the world with Nicoll targeting a top 16 placing
Britain won two bronze medals to take their medal haul for this season's Grand Prix and World Cup events to six, their best ever result.
Laurence Halsted came third in the Tokyo leg of Saturday's Grand Prix.
And the following day Chrystall Nicoll also won a bronze medal in the World Cup series in Koblenz, Germany.
"[This is] already a record for British fencing with several events still remaining," said British Fencing performance director Graham Watts.
"It is particularly pleasing that these medals have been won by four separate athletes in three different disciplines showing that our progress is developing across the weapons."
It was the first time that London-based Halsted, 26, has finished on the podium for a world-ranking event and the medal has boosted his international ranking to 15.
He lost 15-9 to the eventual winner and Olympic silver medallist, Yuki Ota from Japan.
Back-to-back podiums show that my intense training regime is paying off
"Laurence broke the ice today and reached the podium for the first time in a senior Grand Prix," said lead national foil coach Ziemek Wojciechowski.
"It was a major breakthrough and I believe more results will follow."
For Nicoll, 23, it was her second podium placing this month after a third-place finish at the Klagenfurt leg.
The Essex-based fencer narrowly lost 15-14 in Koblenz to Bogna Jozwiak, who went on to win the tournament.
Nicoll said: "The medal in Klagenfurt earlier this month has given me a lot of confidence and I now expect a lot more from myself.
"Back-to-back podiums show that my intense training regime is paying off as I aim for a top 16 world ranking and automatic Olympic qualification."
British Fencing's chief executive Piers Martin added: "The results are coming thick and fast and my congratulations go out to the fencers and their support teams."