May 31 (Reuters) - Britain's competition regulator said on Friday it had started a probe into Nationwide Building Society's proposed 2.9 billion pound ($3.69 billion) all-cash deal to buy Virgin Money UK.

The deal, which was announced in March, could create the country's second-largest savings and mortgage provider.

The Competition and Markets Authority (CMA) said it was considering whether the deal could result in a "substantial lessening of competition" in the UK.

The CMA said the notice on the launch of its inquiry had been sent to the parties, and the regulator has a deadline of 40 days for its Phase 1 decision.

The CMA also invited comments from any interested parties on the transaction by June 14.

Nationwide is the UK's third largest mortgage provider and holds almost 1 in every 10 pounds saved in the UK, as well as one in 10 of the UK’s current accounts. It describes itself as the world's largest building society.

Virgin Money is the UK's sixth-largest retail bank by assets and has around 6.6 million customers.

Responding to the deal's announcement in March, analysts said that the transaction could increase competition in Britain's mortgage and savings market and spur a revival in some bank stocks, which have wilted in the face of geopolitical tensions and lacklustre economic growth. ($1 = 0.7862 pounds) (Reporting by Aby Jose Koilparambil in Bengaluru and Elizabeth Howcroft in London; Editing by Rashmi Aich and Amanda Cooper)