Deprivation is widespread in Jamaica
Mr Sinkinson told BBC Radio 4's Today programme: "It's very difficult to estimate how many passengers on board any flight have got cocaine hidden inside them, but I would think that estimate is probably on the low side."
Jamaica's narcotics police have reportedly agreed, saying "umpteen drugs couriers are travelling from Jamaica to the UK".
And High Commission spokeswoman Mags Fenner reportedly told the Jamaica Observer newspaper that two recent incidents where dozens of Jamaicans were arrested on arrival in the UK were "completely average".
Lucrative rewards
The problem has been blamed on the worsening economic situation on the Caribbean island, and Mr Sinkinson said that most of the smugglers "come from areas of pretty desperate poverty".
"The risks are quite high but in real terms the rewards for the couriers are equally high," he said.
Jamaican drug mules are reportedly paid between £2,000 (J$130,400) and £5,000 (J$335,000) for each trip.
The deputy head of the Jamaican narcotics police, Superintendent Glendon Wright, said a survey last year had shown that 65% of all drugs in the UK had come from Jamaica.
On 17 December 22 Jamaicans were charged with attempting to smuggle a Class A drug after disembarking from an Air Jamaica flight to Heathrow.
Five days earlier, 16 Jamaicans were arrested on suspicion of swallowing cocaine packages after arriving in Gatwick on a British Airways flight.
The arrests were made in a joint operation between British customs and Scotland Yard's Operation Trident, which was set up to tackle "black-on-black" crime.
Lord Harris of the Metropolitan Police Authority told the Today programme that there was a problem, but the statistics suggested by Mr Sinkinson "were frankly unknowable".
He added that it was important to remember that many of the smugglers, most of whom were women, were also victims.
"As far as the drug barons are concerned, the women who do this are totally expendable - that's the really dreadful part of this trade," he said.
Sit and stare
The smugglers who evade customs checks by swallowing the cocaine are also dicing with death.
In October a woman of 30 died on a Kingston to Heathrow flight when one of the 55 packages she had in her stomach burst.
From the end of March a new canine weapon in tackling drug smuggling is being introduced by Customs and Excise.
The "sit and stare" dogs will literally do just that when they pick up a scent from drug smugglers.
The dogs will be able to both search out drugs in the usual way from large areas such as cargo holds, but will also be able to pinpoint the smugglers themselves.
At present customs officers use "passive" dogs for searching among travellers, which sit down next to suspects.
According to the narcotics police, the number of drug mules has increased substantially over the past few years and it is not just Jamaicans who are involved.
The number of UK nationals imprisoned on drugs charges in Jamaica has risen from 20 in 1999 to 150 currently.
Increased usage
Mike Whitlam, of campaign group Prisoners Abroad, said arrest numbers were linked to increased drugs use in the UK.
"Sadly, the UK is a country where drugs are becoming a really serious problem.
"And it is the younger people who are desperate for money who seem to be being arrested."
Detectives estimate up to four tonnes of cocaine is making its way into the UK each year through drug mules.