Thank you for your answer.
He started working for the company in January 2010 at which time we were living in the UK. He has been paying his tax in the UK all this time.
Recently the company's accountant advised the company that he can no longer be on the company's payroll because he is a resident of Hungary therefor he should pay his income taxes in Hungary. This sound like an absolute nonsense to us. The work is in the UK, the company is in the UK and he is a UK citizen. It is true that he does work from home on his computer when he is in Hungary. However he wants to carry on paying his taxes in the UK, because it makes the most sense and we are planing to move back soon.