Blake, a recruitment consultant from Dorking in Surrey, and McRedmond, a welder from Tullamore in County Offaly, were arrested on May 4 after meeting just hours earlier in a hotel bar.
The pair had been knocking back glasses of white wine and vodka at a drink-all-you-like £35-a-head brunch in the Rotana Hotel.
When the brunch finished at 4pm, the pair moved on to the happy hour at the hotel bar before carrying on drinking at the Irish Village pub nearby.
Blake, who admitted drinking four glasses of vodka and five glasses of wine, caught a taxi at 10.30pm outside the bar with McRedmond, who had guzzled "six or seven" vodka drinks.
The Pakistani taxi driver Qaiser Khan, 29, told the court in a written statement that the couple seemed confused and repeatedly changed their minds about where they were going while McRedmond swigged from a bottle.
He said: "I told him it was not allowed to have alcohol inside the taxi but he drank it and threw the bottle out of the window.
"The next thing, I looked in the mirror and saw the woman sitting on the man's thighs.
"She was naked, moving up and down and making sounds."
Mr Khan said Blake moaned for two minutes while writhing on top of McRedmond.
He pulled over when he spotted a police patrol car and called officer Abdullah Obaid Khamis over by beeping his horn and saying: "Come and see what they are doing."
In his witness statement, Mr Khamis said he found the pair still having sex and interrupted them by tapping on the window.
He said: "They kept having sex for four minutes and then I knocked on the glass so they stopped and got dressed.
"The man's shirt was open, his trousers were down to his knees and the woman was not wearing any underwear."
The taxi driver claimed Blake offered him "a lot of money" to tell prosecutors the couple were kissing rather than having sex but he refused.
In the couple's defence, Mr Al Shammary said at the last hearing that there were gaping inconsistencies in the witness accounts. Neither witness gave evidence in the trial, although their statements were submitted to judges in the misdemeanours court.
The lawyer said the pair could not have been having sex because Blake was on her period at the time, adding: "This is Dubai, not a mosque. Everyone drinks."
The pair pleaded not guilty to charges of having consensual sex and indecency, which related to stripping off in public, but were convicted on both counts.
They are the latest Britons to fall foul of the United Arab Emirates' strict Islamic laws preventing drunkenness in public and sex outside marriage.
In 2008, Vince Acors, 38, and Michelle Palmer, 40, were convicted of indecency and jailed for three months after being caught having sex on a beach. The sentence was suspended on appeal.
In 2009 Charlotte Adams and Ayman Najafi spent a month behind bars after an Emirati woman complained they were kissing in public.