June 10 (Reuters) - Britain's Mitie on Thursday predicted its full-year profit would beat current market estimates, as the facilities management provider benefits from COVID-related work and earnings from its new Interserve division.

Mitie, which provides security, cleaning and engineering services to corporate and government organisations, said it was also seeing early signs of revival in its engineering services business as the pandemic eases.

"As businesses slowly start to reopen and our customers' employees return to offices, we are starting to see some green shoots of recovery," Mitie Chief Executive Officer Phil Bentley said in a statement.

Mitie has been providing security services in virus quarantine hotels and helped the government roll out hundreds of COVID-19 testing sites across the United Kingdom, cushioning a decline in revenues from engineering projects and maintenance as customers such as Rolls Royce and Heathrow cut spending.

Its operating profit for the year ended March 31 tumbled 26% to 63.4 million pounds ($89 million), but beat analysts' average expectations of 58.8 million pounds. Revenue, which rose 18%, thanks to the Interserve deal, also topped expectations.

However, Mitie shares rose 5.3% to 75.5 pence by 0812 GMT on the upbeat outlook.

Following its update, Peel Hunt analysts raised their Mitie profit estimates for the year ending March 2022 by 26% to 103 million pounds ($145 million). Mitie itself did not provide specific estimates for annual profit.

Revenue from Mitie's dominant cleaning and security services grew 10% in fiscal 2021 as food retail and logistics customers spent more.

Bentley, who took charge of Mitie in late 2016, has been cutting costs after a string of profit warnings that year.

The first stage of Mitie's transformation aimed at "fixing the business" was now complete, Bentley said in an interview, adding that the next phase would focus on growth.

Over the medium term, Mitie is targeting mid-single-digit revenue growth on percentage terms and profit margins of 4.5% to 5.5%.

Mitie also raised its targeted cost savings from the purchase of collapsed rival Interserve's facilities management business to 42 million pounds from 35 million. ($1 = 0.7096 pounds)

(Reporting by Yadarisa Shabong in Bengaluru; Editing by Ramakrishnan M. and Emelia Sithole-Matarise)