Two of the migrants intercepted off the Norfolk coast had previous convictions for murder and drug offences and were "removed immediately", it has emerged.
And a further five "came to the attention" of law enforcement once they were brought to land.
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Of the 69 attempting to cross to the UK 67 were males and two were pregnant women.
A handful were brought over as "debt bondage" and destined to work for gangs to pay off money they owed.
It is understood the man with a conviction for drugs offences had previously been deported.
The details have emerged following the conviction on Wednesday of four men Igor Kosyi, Alexsandrs Gulpe, Kfir Ivgi and Sergejs Kuliss who were found guilty of conspiring to facilitate illegal immigration at Chelmsford Crown Court.
They will hear their fate on December 21 when they are due to be sentenced.
A Home Office spokesperson said it would not comment on the fate of the migrants, who travelled in a boat condemned as a "death trap".
A statement said: “Migrants that enter the country illegally will be subject to the UK’s immigration rules.
“As we move forward with the New Plan for Immigration, how somebody arrives in the UK will impact on how their asylum claim progresses, and on their status in the UK if that claim is successful.”
Albanian nationals need a visa to enter the UK. It is understood the 69 migrants were without paperwork.
Keith Mursell of Caister Coastwatch said volunteers scanning the seas were always on the lookout for people or boats in distress or anything suspicious.
But on the day the fishing trawler Svanic was intercepted trying to smuggle the Albanians into the UK on November 17 the country was well into its second lockdown and there were no volunteers on duty.
He said the gang would likely have struggled to unload the migrants anywhere along the coast without being detected as any vessel entering the waters without announcing itself would be challenged.
Being on the lookout for illegal immigrants was part of their remit, he added, but only a larger boat would be able to navigate the treacherous North Sea.
Richard Goffin port director for Peel Ports, Great Yarmouth, said he was aware of the incident and had supported the investigation.
However, areas beyond the entrance to the river and outer harbour were not governed by the port which was currently operating under the lowest alert level.
The journey of the 69 migrants and the ship's crew of three inexperienced men started in Latvia.
On its way to pick up the Albanians in Ostend in Belgium the vessel ran aground off the Swedish coast - raising suspicions among the coastguard team.
It was monitored by Border Force agents and stopped off Yarmouth leading to a high profile investigation into organised crime gangs (OCG) which concluded at Chelmsford Crown Court.
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