They were followed on the court at Horse Guards Parade, the spectacular Olympic venue a stone's throw from Big Ben, by Americans April Ross and Jennifer Kessy who defeated Liliana Fernandez and Elsa Baquerizo of Spain in a three-set thriller.
Earlier, men's favourites Emanuel Rego and Alison Cerutti of Brazil breezed through a clash against Italians Paolo Nicolai and Daniele Lupo to come top of their group after three wins.
Mullin and Dampney, who won their first pool match and lost the next two, still have a chance to go through to the knock-out phase, which starts on Friday. For that, they need to win a "lucky loser" match later against another third-placed team.
The Britons were ahead for much of the first set against Evgenia Ukolova and Ekaterina Khomyakova, earning three set points that they were unable to convert.
In beach volleyball, the first two sets are played to 21 points and the third to 15, but a two-point advantage is required to win.
The first set of the British-Russian match went to 25-23 and despite vociferous support from a sea of spectators who cheered, stamped their feet and danced the conga to encourage them, Mullin and Dampney lost the second by 21-13.
"That was a match we wanted to win to get into the top 16 and not have to play this evening so we could recover, so now we have to go back, lots of hard work to do before the match tonight," Mullin told reporters.
The normally cheerful and chatty Dampney, who gained a fervent following among young British men by posing in the nude for GQ magazine before the Games, was visibly upset.
"We'll relax, we'll obviously be talking to our coaches, we'll eat, we'll stretch, we'll just make sure we're in the best frame of mind to go out fighting again tonight," she said.
Beach volleyball is not played by many people in rainy Britain. Dampney and Mullin both started out in indoor volleyball and used to played against each other when Dampney was in the England team while Mullin played for Scotland.
The pair have received quite a lot of attention from the British tabloid press, not least because they sport mini British flags on the back of their bikini bottoms and have painted their nails in elaborate patterns of patriotic blue, white and red.
Americans Ross and Kessy, considered strong contenders for a medal in the women's event, saved several match points against Baquerizo and Fernandez and needed multiple chances of their own to finally defeat the Spaniards by 2-1 (19-21, 21-19, 19-17).
It was one of the most evenly matched contests in the tournament so far and had the crowd jumping up and down.
Kessy and Ross have spent much of their careers in the shadow of compatriots Misty May-Treanor and Kerri Walsh, the only pair of either gender to have won Olympic gold in beach volleyball twice.
Both American women's pairs go into the knock-out phase undefeated, as do their main rivals, reigning world champions Juliana Felisberta and Larissa Franca of Brazil.
There are 24 teams per gender competing in the beach volleyball event, split into pools of four. The last of the pool matches are due to take place later on Thursday.
In each gender, the top two teams in each pool go through to the knock-out phase as do the two third-placed teams with the most points. The remaining third-placed teams play in the lucky loser matches scheduled to take place on Thursday night.
In the men's event, reigning world champions Emanuel and Alison of Brazil beat Nicolai and Lupo by two sets to nil on Thursday morning to confirm their status as favourites.
Five-time Olympian Emanuel won gold with his former team mate Ricardo Santos in Athens in 2004. Ricardo is also competing in London with his own new partner, Pedro Cunha, and they too emerged undefeated from the pool phase.
The Brazilians' main rivals for the men's gold are two American pairs, Beijing gold medallists Todd Rogers and Phil Dalhausser on the one hand and Sean Rosenthal and Jake Gibb on the other.