The BBC's former head of news, who took over the reins at Covent Garden at the beginning of the month, will meet union officials in an attempt to avert the strike, which could threaten forthcoming productions including La Traviata, The Queen of Spades and Otello.
About 80% of Bectu members who voted in the ballot have backed industrial action over the way ROH management has dealt with Pat Styles, a shop steward who was suspended in January after some members of staff accused him of aggressive behaviour and bullying. The union claims it is Mr Styles's position as a union official that lies behind the disciplinary hearings and says it is not the first time union representatives have come under pressure at the Royal Opera House.
Gerry Morrissey, assistant general secretary of Bectu, said: "We hope that these talks will be successful, but this will depend on the management's attitude. We hope that Tony Hall will bring home to the management a sober recognition that, as a publicly funded body, the opera house cannot afford to wage war on its workers' trade union."
But management at Covent Garden, who instituted disciplinary procedures against Mr Styles that had to be postponed due to his ill health, said the allegations of bullying and intimidation had been made by other members of staff, including some Bectu members.
"It seems the union feels it is inappropriate for someone who is a union official to be subject to the same procedures as any other member of staff. But that is not the view of the ROH management," a spokesman said.
The spokesman said that nearly half of the Bectu members had not voted, and only 43% of the total voted yes.
So far Mr Hall has not been personally involved in the dispute, which was initially handled by John Seekings, acting executive director after the departure of Michael Kaiser in December.
Talks at the conciliation service Acas have not resolved the issue, and the union has called on management to accept a compromise involving both sides taking part in a programme of training in negotiation techniques and human resource management.
Any concessions at Acas this week are likely to be hard fought. Mr Hall, 49, is seen as a hard-nosed administrator.
Mr Morrissey said: "Initially we are not going to set out to cause performances to be cancelled, but it may get to the stage where we have no alternative."