LONDON, July 31 (Reuters) - Britain has appointed Richard Moriarty as new chief executive of the Financial Reporting Council (FRC) from October, though it is still unclear when the watchdog will be transformed into a long-promised tougher regulator following a string of accounting scandals.

Moriarty has spent 20 years at various regulatory bodies, including most recently as chief executive of the Civil Aviation Authority, and has also been CEO of the Legal Services Board.

He replaces Jon Thompson, who had already announced he was stepping down after four years to chair rail project HS2.

The business ministry said Moriarty would continue with the work begun by Thompson to transform the FRC into a new regulator, the Audit, Reporting and Governance Authority (ARGA), though a formal legal underpinning is needed for it.

ARGA is among the recommendations from three government-backed reviews into auditing after the collapse of builder Carillion and retailer BHS raised questions over audit quality.

The government said in December 2019 it would develop proposals to create a "strong regulator" and implement other recommendations from the reviews.

The business ministry has said it would table legislation when parliamentary time allowed, though a general election is widely expected next year. (Reporting by Huw Jones Editing by Jon Boyle and Mark Potter)