Adds CEO quotes in paragraphs 5-6, 9, shares in paragraph 8

By Paul Sandle and Sarah Young

LONDON, Feb 5 (Reuters) - BT BT.L, Britain's biggest telecoms group, said it was seeing record demand from homes and businesses wanting to connect to its growing fibre network, helping reduce its overall customer losses.

The group has been losing customers from its national Openreach fibre network to smaller rivals, but is increasing the number moving to faster full fibre, boosting profitability.

BT, which serves broadband and mobile markets with its BT, EE and Plusnet brands and provides the network used by Sky, TalkTalk and Vodafone, said it added 571,000 net fibre connections, up 21% year-on-year, in its third quarter.

Line-losses on its Openreach network, which competes with Virgin Media and "altnets" like CityFibre, were 210,000, better than the previous quarter and reducing its annual losses forecast to around 850,000 from a previous 900,000.

Chief Executive Allison Kirkby said BT was both building its network, which now reaches more than 21 million properties, and connecting customers at pace.

"The reason line-losses are starting to abate is the fact that we are still building and others are not," she said.

Virgin Media, jointly owned by Telefonica and Liberty Global, and CityFibre are increasingly looking to deploy capital on consolidation rather than laying fibre.

'LIMITED' IMPACT FROM SKY SWITCH

Shares in BT, which have risen 44% in the last 12 months, gave up early gains to trade down 0.7% at 1300 GMT.

Kirkby said the impact of its major customer Sky joining the CityFibre network in addition to Openreach last year had been limited, with no year-on-year deterioration in line-losses for two quarters in a row.

For the three months to the end of December, BT reported a 4% drop in revenue, driven by lower service revenue and weaker handset sales, and a 1% drop in adjusted core earnings to 2.1 billion pounds, in line with forecasts.

The group said it was confident of meeting guidance, including its target for cash flow to reach 2 billion pounds next year and 3 billion pounds by the end of the decade.

($1 = 0.7343 pounds)

(Reporting by Sarah Young and Paul Sandle; Editing by Kate Holton and Elaine Hardcastle)

((sarah.young@thomsonreuters.com; +44 20 7542 1109; Reuters Messaging: sarah.young.thomsonreuters@reuters.net))