A suspected people smuggler has been arrested in Britain after DNA allegedly linked him to a van involved in a police shootout that killed a two-year-old girl whose migrant family was trying to reach the UK from Belgium.

Mawda Shawri, who was sitting in her mother’s lap, was shot in the face after a high-speed chase when Belgian officers tried to shoot the Peugeot van’s tyre in May. The driver, suspected of trying to smuggle 26 adults and four children into Britain, fled the scene.

It emerged on Monday that a 25-year-old Iraqi man was arrested in the UK. His DNA allegedly matches that found on the van’s steering wheel and Belgian authorities are expected to use a European Arrest Warrant to extradite the man.

Selma Benkhelifa, a lawyer acting for the parents of the girl, whose death sparked protests in Belgium, which has taken an increasingly hard line against migrants, said: “You have to try to find out if he was really a human trafficker or if he was just the little hand of the network. And if that’s the case, you have to try to go higher in the hierarchy.”

On Tuesday, Belgian media reported that the Kurdish girl’s life could have been saved through better communication between Belgian and French police forces.

French officers knew the van was involved in human smuggling, according to the De Morgen newspaper, and had been tracking it with a GPS tracker.

Judicial sources suggested that pursuing officers would have treated the chase differently if they had known the van was carrying so many people.

An officer is under investigation for the killing.