Data obtained under Freedom of Information laws from the Home Office indicate 1,156 people were recorded as making such a claim between January and June 2022.
Of these, 591 were Albanian, according to figures provided by the department following a request from campaign group Migration Watch.
Official Home Office figures show 12,747 migrants crossed the Channel by the end of June last year. This suggests about 9 per cent of arrivals during that period claimed to be victims of modern slavery.
The number of Albanians who said they were modern slavery victims in the first six months of 2022 is more than double the figure for the whole of 2021, according to the data.
In that year, 218 out of 1,946 people claiming to be victims of modern slavery were recorded by the Home Office as being Albanian.
UK coastguard responds to migrant emergency in English Channel — in pictures
Other nationalities during that period included 478 Vietnamese, 286 Eritreans, 222 Iranians, 220 Sudanese, 123 Iraqis and 64 Afghans.
The statistics were taken from a live database, so could change as the system is updated, and the numbers are likely to increase at some point as modern slavery can happen, or be reported, at any time, the department said.
Migration Watch chairman Alp Mehmet claimed Albanians “and their traffickers have identified a huge loophole in our legislation and are exploiting it to the hilt”, adding to the “great pressure that the already overwhelmed system is under”.
But Mark Davies, from the Refugee Council, warned it was “dangerous to assume all Albanians are falsifying modern slavery claims” and said every case should be “given a fair assessment”.
“The situation with people from Albania crossing the Channel is complex,” he added. “We know from our work that trafficking and exploitation are a problem for many from the country.”
The findings come as the Home Office said it had removed 43 Albanians on a deportation flight on Thursday.
Migrants at immigration processing centre in Manston — in pictures
Twenty-seven were foreign national offenders convicted of crimes including drug dealing, burglary, fraud, embezzlement and robbery. The remainder were immigration offenders. The group included six people known to have arrived in the UK after crossing the Channel, the department said.
“We are working around the clock to remove those with no right to be here. This is a crucial part of our plan to keep communities safe and to restore fairness to our asylum and immigration system,” said immigration minister Robert Jenrick after the flight.
Last month, Prime Minister Rishi Sunak vowed to deport thousands of Albanians under plans to tighten modern slavery laws.
Mr Sunak told MPs how 400 new specialists will work in a dedicated unit expediting asylum claims from people from the Balkan state, with plans for weekly removal flights to take people back to their home country.
Ministers singled out Albanians as accounting for more than a third of the 33,000 migrants who crossed the Channel in the first nine months of 2022 — a sharp increase compared with the 3 per cent recorded in the whole of 2021.
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Mr Sunak recently held his first talks with Albanian Prime Minister Edi Rama, during which they agreed to close “loopholes” preventing the rapid return of failed asylum seekers.
But Mr Rama has been angered by comments from Home Secretary Suella Braverman, whom he said was using his citizens as scapegoats for failed immigration policies.
Albanian ambassador to the UK Qirjako Qirko also called for an end to the “campaign of discrimination” against Albanians living in Britain as he was grilled over the rise in numbers crossing the Channel.
Mr Sunak insisted Albania was a “safe, prosperous European country” but MPs previously heard a third of citizens live below the poverty line.
Andi Hoxhaj, a lecturer in law from University College London, also told the Commons Home Affairs Committee that there was 60 per cent youth unemployment among 18 to 34-year-olds in the country as he warned of problems with blood feuds, corruption and gang violence.
Earlier this year, two former commissioners warned plans to reform modern slavery laws could reduce protections for victims.