The former Northern Ireland international was admitted to Cromwell Hospital in west London last month where his condition deteriorated and he was taken to intensive care.
Until recently he had been improving but he has now taken a turn for the worse and was admitted to intensive care yesterday morning from a ward, Professor Williams explained.
Outside the hospital he said: "Mr Best is not so well. He has been admitted back to intensive care. He has got a new and severe infection. He is on dialysis and he is very poorly.
"He was improving every day until yesterday afternoon and he was really pretty good. He was maintaining some progress each day and now he has acquired another infection as these patients are very susceptible to infection at this stage of recovery."
Best's infection is causing problems "with kidneys and everything else again". He added: "His breathing is OK. He is having oxygen but he is not on a ventilator. It is a big setback after some steady progress over the last two weeks."
Professor Williams said that he did not know how long Best would be in intensive care but he was hoping the infection would respond to antibiotics.
"He is conscious and just about talking. He is eating and was making good progress but we are all very disturbed at a sudden setback like this," he said.
"We are not sure where the infection is. There are so many places it could be." Asked if the current infection was life-threatening, he said: "He is very ill at the minute, so we'll see how it goes during the day."Reuse content