The development follows a stabbing in Golders Green, North London, on Wednesday.
The UK makes it quicker to return Nigerians with no legal right to remain.
Mr Tunji-Ojo acknowledged that Nigeria had an existing, commendable working relationship with the UK Home Office.
Study visas for nationals from Afghanistan, Cameroon, Myanmar, and Sudan have been halted, as have work visas for Afghans.
Reuters said groups of inmates were seen walking out of Brixton, Durham and Liverpool jails, and around 400 prisoners are reportedly due to be freed from London prisons
