LONDON - Britain on Wednesday said a barrister had been appointed to lead an independent investigation into Deputy Prime Minister Dominic Raab after two formal complaints about his behaviour, the latest case of alleged bullying in government.

Adam Tolley, a barrister at Fountain Court Chambers, will lead the investigation, the terms of reference published by the government said, without saying when it would be completed.

"The investigation should be completed as swiftly as possible and the investigator will proceed on this basis," the government said. "The report of the investigation will be made public."

Raab said in a letter to Sunak a week ago that he had been notified of two separate complaints, one from when he was foreign minister and one from his tenure as justice minister.

He requested an independent investigation into the complaints.

Some officials who have worked for Raab say he was a tough and demanding boss, with others being quoted by local media as saying he was rude, aggressive and a bully. Raab has denied the allegations.

Sunak used his first speech as prime minister last month to say his government would demonstrate "integrity, professionalism and accountability".

The terms of reference of the investigation say the final judgement on whether Raab was in breach of the ministerial code will be made by the prime minister.

Sunak has defended his deputy, saying he did not recognise allegations that Raab had bullied staff.

Earlier this month, cabinet minister Gavin Williamson resigned from government over allegations he had bullied colleagues, with opposition parties saying the case raised questions about Sunak's judgment just weeks into the job.

(Reporting by Alistair Smout. Editing by Andrew MacAskill)