NSW Premier Gladys Berejiklian has made the stark admission that her government will lose the impending byelection triggered by a Nationals’ MP’s sex scandal.

“If you look at the history of by-elections in NSW, there has been at least a double-digit swing against governments and certainly it would take more than a miracle for us to keep the seat,” Ms Berejiklian said on Thursday.

“Of course we will try.”

The early exit of Michael Johnsen on Wednesday has left the Premier to deal with a minority government.

Mr Johnsen quit his marginal Upper Hunter seat after a week of mounting pressure for him to resign after admitting he was being investigated for raping a sex worker in 2019.

He strenuously denies the allegation but he is also facing allegations he offered a prostitute $1000 to have sex with him at his parliament house office, exchanged lewd texts with her and sent her an obscene video while sitting in the parliamentary chamber.

Ms Berejiklian said she had resigned herself to the fact it will be virtually impossible for the Coalition to retain the seat. Mr Johnsen holds it for the Nationals by a margin of just 2.2 per cent.

“I have no doubt we won’t retain the seat,” Ms Berejiklian said.

“If you just look at the maths, on average, the swings against governments in byelection in the last 10 years since we have been in government have been between 10-15 per cent.

“I have very little confidence we will retain the seat, but that is not to say we won’t put a strong case. We will put our best foot forward but the maths are against us.”