The three Kenyans won a ruling from Mr Justice McCombe last year that they had "arguable cases in law".
But the case came back to London's High Court in July to consider a claim by the Foreign and Commonwealth Office that the actions were brought outside the legal time limit.
Lawyers for Wambugu Wa Nyingi, Paulo Muoka Nzili and Jane Muthoni Mara argued that it was an exceptional case in which the judge should exercise his discretion in their favour.
Today, Mr Justice McCombe said they had established a proper case for the court to exercise its discretion and allowed their claims to proceed to trial.
More top news
Mr Trump addressed thousands of supporters in Florida on Tuesday and responded to the mixed reviews he received during the debate.
Parents in Anglesey, North Wales, will have to show birth certificates in order to prove their child's age and qualify for the scheme.
Former Israeli president Shimon Peres dies, aged 93, following a stroke two weeks ago.