GB will have 10 crews in the finals - more than any other nation - after the lightweight men's double scull and lightweight men's four both qualified.
Double scullers Zac Purchase and Mark Hunter won their heat to maintain their impressive unbeaten streak this season.
The four qualified despite being pushed into third by defending champions Denmark and the fast-finishing French.
There was disappointment for Helen Casey and Hester Goodsell, who missed out in the women's lightweight double.
They came fifth in their semi-final to drop into the B final - only they and the men's openweight pair from the GB squad missed out on A finals.
Purchase and Hunter became the first lightweight British crew ever to qualify for an Olympic final after dominating their semi-final.
"We went out hard and made sure that we led rather than being led. The last 750m was quite enjoyable," Hunter told BBC Sport.
Greece were five seconds faster, winning the other semi-final in 6 minutes 24.61 seconds, but the GB duo were nonplussed.
"It's time for a bit of relaxation and preparation for the last 2000m of the season and also the fastest 2000m of the season," said Purchase.
In the four, Richard Chambers, James Lindsay-Fynn, Paul Mattick and James Clarke faded a little after an impressive first 1500m, coming through in 6 min 08.7 sec.
Former world champions and event favourites China missed out on a final spot and were dramatically pushed into fifth in a semi-final won by Poland.
"We had to go out hard from 250m to 750m as we had the gold, silver and bronze medallists from last year's world championships," said strokeman Clarke.
"Maybe we paid the price in the last bit of the race, but the whole thing was to get in the final."
Great Britain's women's lightweight double were in a similar position and were both clearly upset afterwards.
"We went into it thinking if we did our absolute best we might be able to do it.
"Obviously we didn't put it together and we're really upset," a tearful Goodsell told BBC Sport.
But Casey said: "We gave it our best shot. It's really gutting not to make the final but we were outside chances to make it and we've had our two best races together."
The lightweight semi-finals had been delayed by 24 hours because of thunderstorms on Thursday.
Italy and Poland look the favourites in the men's quadruple sculls - the only event that Great Britain did not enter - after both won their semi-finals.
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