The Home Secretary said people smugglers are “treating innocent lives as a commodity and lining their pockets while people are dying” as the dawn raids were carried out on Wednesday.
The men, aged 52 and 28, were held on suspicion of conspiring to facilitate illegal immigration during a National Crime Agency (NCA) swoop in Woodford Green and Bushwood, east London.
Another five people who are all licensed minicab drivers were also arrested for allegedly moving migrants to and from lorry drop-off or pick-up points.
Investigators also found a safe house in Mile End with bunk beds crammed into every room where 11 suspected migrants were found.
In March Ms Patel revealed plans to crack down on people smuggling with maximum life sentences for such criminals in the biggest overhaul of the UK’s asylum system in decades.
She also announced moves to deny asylum to migrants who have travelled through a “safe” country such as France to reach the UK.
Wednesday’s operation involved more than 130 officers following Operation Symbolry.
The investigation delves into an organised crime group using a network of predominantly Romanian lorries to smuggle people between France and the UK.
Vulnerable migrants were found hidden in the back of their trucks and five lorry drivers have already been convicted in relation to the investigation.
More than 100 migrants were discovered during the operation including three suspected criminals who were trying to flee the UK, the NCA said.
“The penalties for drivers caught smuggling migrants are severe and I would ask those tempted by the idea to consider the potential impact on their lives and livelihoods,” NCA branch operations manager Chris Hill said.
“We believe the arrests today, coupled with the actions we have already taken, will end the activities of that network.
“Organised crime groups often rely upon enablers such as complicit lorry drivers and minicab drivers to carry out their work, offering them money to help.”
The NCA has around 50 ongoing investigations into people trafficking and organised immigration crime.
NCA deputy director of investigations Chris Farrimond said: “People smugglers are ruthless, treating migrants as a commodity, and they do not care about the safety of those they transport. We have seen this, tragically, in recent and historical mass fatalities.”