No more than seven people will be on Tuesday’s flight as four men lose appeals at the High Court.
Boris Johnson has defended plans to fly asylum seekers to Rwanda as some due to be on the first flight failed in their bids to avoid being removed.
Up to eight people are due to be on Tuesday evening’s flight but appeals against removal are being heard.
The PM said he had always known the scheme would attract “plenty of legal challenges” and said the government may “very well” need to change the law.
The Church of England and human rights groups have criticised the plan.
Mr Johnson said he had long believed the scheme was a “long process” with potential bumps in the road and earlier accused lawyers representing migrants of “abetting the work of criminal gangs”.
The cases lodged on behalf of people set to be flown to the east African nation’s capital Kigali will be heard before the flight departs, after a last-ditch attempt to block the flight altogether was rejected by the Court of Appeal on Monday.
This judgement was subsequently upheld by the Supreme Court on Tuesday.
A No 10 spokesman said, given the legal challenge, he could not be definitive that the flight would leave on Tuesday but earlier, Foreign Secretary Liz Truss had insisted that Tuesday’s flight would leave.
On Monday, 138 people reached the UK in three boats, with more than 10,000 migrants recorded as making the dangerous journey so far this year.
One man has failed in his bid not to be removed from the UK to Rwanda on Tuesday, while a number of other legal challenges are ongoing.
Speaking to cabinet ministers earlier, Mr Johnson said the government was “going to get on and deliver” on its plan.
He told ministers the objective was to ensure there was a “clear distinction” between immigration to the UK by safe and legal routes that the government supports and “dangerous and illegal cross-Channel migration, which we intend to stop”.
The flight on Tuesday evening was originally due to carry dozens of passengers, but most have succeeded in their individual appeals against removal.
It is 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.
Before Mr Johnson addressed cabinet, Ms Truss told the BBC the flight would leave even if a very small number of people were on it, as it would “establish the principle” of the policy to break the business models of people traffickers.
“If people aren’t on the flight today, they will be on subsequent flights to Rwanda,” she said.
She also declined to say how much the flight would cost, but argued the cost of human trafficking and illegal immigration was “huge” to the taxpayer.
There is not nearly as heated a debate in Rwanda about the relocation of asylum seekers as there is in the UK.
Critics of the Rwandan government say this muted response is unsurprising, citing limited freedoms.
They also point to Rwanda’s human rights record, which the government has defended. Government spokeswoman Yolande Makolo added that the asylum seekers would be “as free as any Rwandan” during their stay.
If the relocation goes ahead, their claims for asylum are to be handled by the Rwandan government under domestic and international laws.
They will be accommodated at the Hope Hostel, which until recently was the home for survivors of the 1994 Rwandan genocide who were orphaned at the time. Opposition leader Victoire Ingabire told the BBC the decision to move them to make room for the asylum seekers was “unfortunate”.
In a letter to the Times, 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 that “those to be deported to Rwanda have had no chance to appeal, or reunite with family in Britain”.
“They have had no consideration of their asylum claim, recognition of their medical or other needs, 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.
They will get accommodation and support while the Rwandan government considers their application, and if they are successful they can stay in the country with up to five years’ access to education and support.
If their asylum claim is unsuccessful, they will be offered the chance to apply for other immigration routes, but could face deportation from Rwanda.