Three more people due to be on the first flight taking asylum seekers to Rwanda are planning legal challenges before take-off later on Tuesday.
They are among eight people still on the passenger list after dozens won legal cases and were removed.
A last-ditch attempt to block the flight altogether was rejected by the Court of Appeal on Monday, however.
The flight is likely to cost more than £500,000, but ministers say it will disrupt the business of traffickers.
As the archbishops of Canterbury and York joined opposition politicians in condemning the plan, a government spokesman acknowledged more last-minute legal challenges were expected but said "we will not be deterred" from starting the flights.
Pressing ahead with the policy of transporting asylum seekers to the east African nation would "break the business model of vile people smugglers" and "ultimately save lives", a spokesman said.
The flight on Tuesday evening was originally due to carry dozens of passengers, but most succeeded in their individual appeals against deportation.
It was not clear exactly how many will leave on the flight: on Monday night, the Home Office said it was eight, while the charity Care4Calais said the number had fallen to seven.
In , senior Church of England leaders described the plan as an "immoral policy that shames Britain".
Signed by the archbishops of Canterbury and York and more than 20 other bishops who sit in the house of Lords, the letter said those being deported have had "no consideration of their asylum claim... or any attempt to understand their predicament".
Tuesday's flight is due to be the first in a five-year trial, in which some asylum seekers deemed to have entered the UK illegally are transported to Rwanda to claim refuge there.