A family of asylum seekers from Yemen who were told they could not remain together in the UK because the father travelled to the country by plane and his three sons arrived by small boat have been told their case will be considered together after a Home Office U-turn.

The government change of heart emerged days after an announcement from the home secretary that how people enter the UK would have a bearing on the progress of their asylum claim. Priti Patel said asylum seekers should stay in the first safe country they arrive in rather than travelling onwards to the UK.

The family, who have asked to be referred to by their first names only, had been living in a Gulf state, but when that country revoked their residency permits they were forced to flee.

Although all four asylum claims are based on the risk to their lives in Yemen, the father, Hussein, 52, was able to travel by plane to the UK as he obtained a visitor visa. His journey from the Middle East to the UK took a few hours and did not endanger his life.

But his three sons, Hamzeh, 26, Hassan, 24, and, Hazem, 22, were unable to obtain visas and so had to use smugglers to reach the UK. Their journey took a year, cost far more than their father’s journey and put their lives at risk many times over.

The father reached the UK before his sons did. They were overjoyed when they made contact with each other and the Home Office agreed to place the family in accommodation together in Manchester. However, the Home Office later arrested and detained the three sons and said they would be removed to Spain, a country they had passed through before reaching the UK.

Hussein said he had cried throughout his sons’ dangerous journey to the UK. “I felt so worried about their survival all the time and I felt so guilty that my journey was so much easier than theirs,” he said.

Hassan said the family was hugely relieved after being informed by the Home Office that the three sons were no longer facing separation from their father and removal to Spain.

They are learning English through the Prince’s Trust and a local college and are volunteering at FareShare.

“A heavy weight was lifted from our hearts when we got this news,” he said.

The family’s solicitor, Hannah Baynes at Duncan Lewis, said: “We are pleased that after months of uncertainty, the Home Office has agreed that Hassan, Hamzeh and Hazem’s asylum claims can be considered in the UK and that there are no longer any plans for them to be removed to Spain.

“The past few months have been particularly stressful for them, and so it is good news that the brothers can now remain living in the UK with their father, whose asylum claim is already being processed in the UK. It is unclear exactly why the Home Office decided to do this; all that we have been told is that this is due to their individual circumstances.”

Home Office sources said coronavirus travel restrictions meant it was not possible to facilitate the return of Hazem, Hassan and Hamzeh before the end of the Brexit transition period and that their asylum claims were now being progressed in the UK.

Sonya Sceats, thechief executive of the charity Freedom from Torture, said: “This government is seeking to divide families and create chaos with its cruel new proposals. We must remain a place of safety for people fleeing persecution, and give protection according to need, not means of arrival. Now more than ever, it’s important we stand for humanity and fairness.”

A Home Office spokesperson said: “It is an established principle that those in need of protection should seek asylum in the first safe country that they enter and not put their lives at risk by making unnecessary and dangerous onwards journeys to the UK. Our new plan for immigration will overhaul our asylum system and make such claims inadmissible.”