UPDATE 7-UK's Labour plans high-speed connection to voter hearts with BT nationalisation

* Labour promises free fibre broadband for all

* Labour to nationalise BT's fixed line network

* UK PM calls it "crazed Communist scheme'

* Labour to tax Google, Amazon and Facebook to pay

* Labour suggests other telecoms could be nationalised (Adds Johnson and EU state aid rules)

By Guy Faulconbridge and Paul Sandle

LONDON, Nov 15 (Reuters) - Britain's opposition Labour Party plans to nationalise BT's broadband network to provide free internet for all if it wins power, making a radical election pledge to roll back 35 years of private ownership that caught both the company and its shareholders by surprise.

Labour's proposed overhaul of the telecoms infrastructure, an addition to its already broad nationalisation plan, would be paid for by raising taxes on tech firms such as Alphabet's Google, Amazon and Facebook and using its Green Transformation fund.

The announcement by Labour, which is currently lagging Prime Minister Boris Johnson's Conservatives in opinion polls ahead of the Dec. 12 election, sent BT's shares down as much as 3.7%, wiping nearly half a billion pounds off its market value. The share was down 1.7% at 1410 GMT.

Labour plans to nationalise Openreach - the fixed-line network arm of the country's biggest broadband and mobile phone provider - as well as parts of BT Technology, BT Enterprise and BT Consumer to create a "British Broadband" public service.

"A Labour government will make broadband free for everybody," Labour leader Jeremy Corbyn said in a speech. "This is core infrastructure for the 21st century. I think it's too important to be left to the corporations."

"We'll tax the giant corporations fairly - the Facebooks and the Googles - to cover the running costs," said Corbyn, adding the public had been forced to pay far too much for "rip-off broadband" and the party would transform the British economy.

BT, with roots in an 1846 telegraph company, was once one of Britain's national champions and the flagship of Margaret Thatcher's privatisation policy when it was floated by her Conservative government in 1984.

Labour's announcement brought into sharp relief the election stakes: Johnson who promises to deliver Brexit in January or Labour which says it wants to be the most radical socialist government in British history.

The relatively muted market reaction indicates investors do not expect Labour to win, analysts said. BT also retained the right to show UEFA Champions League soccer games, helping to support shares.

Johnson derided Corbyn's plan, saying it would undermine the world's fifth largest economy and cost taxpayers dearly. He has promised to roll out full-fibre broadband to all homes by 2025.

"We are funding a huge programme of investment in our roads, in telecoms, gigabyte broadband, unlike the crazed, crazed Communist scheme that was outlined earlier on today," Johnson told Conservative Party activists.

The Conservatives said Corbyn's plans would be illegal under EU rules governing state aid.

Labour said the cost of nationalising parts of BT would be set by parliament and paid for by swapping bonds for shares.

'VERY, VERY AMBITIOUS IDEAS'

In what would amount to the biggest shake-up in British telecoms since Thatcher's privatisations of the 1980s, Labour said few would lose out while millions would benefit.

The national Openreach network is also used by BT's rivals, including Sky, TalKTalk and Vodafone, to provide broadband to their own customers. Its only competitor with widespread coverage is Virgin Media, owned by Liberty Global.

TalkTalk said on Friday a deal to sell its FibreNation business had stalled after Labour's announcement.

Labour's second most powerful man, John McDonnell, suggested that the owners of the networks that compete with Openreach, such as Virgin Media's cable network and new fibre providers, could come to an arrangement or be nationalised too.

"We'll come to an agreement with them. It will either be an agreement of access arrangements, or working alongside us, or if necessary they can come within the ambit of British Broadband itself," McDonnell said.

Labour, led by 70-year-old socialist Corbyn, has been open about its plans to nationalise the rail, utility and water companies as well as to increase taxes on the wealthy, but has never previously suggested nationalising BT's assets and the company was taken by surprise.

"These are very, very ambitious ideas and the Conservative Party have their own ambitious idea for full fibre for everyone by 2025 and how we do it is not straightforward," Chief Executive Philip Jansen told the BBC.

BT CRITICISED

Currently, fewer than 10% of British premises have access to full-fibre broadband - also called fibre to the premises - where fibre optic cable instead of copper is used to connect homes to the network.

BT has been criticised by customers, rivals and the regulator for poor service and a lack of ambition in upgrading its network to fibre, where Britain lags far behind European countries like Spain.

Labour said it would roll out the free broadband to all individuals and businesses by 2030, providing it to at least 15 million to 18 million premises within five years. It said the plan would save the average person 30.30 pounds a month.

There would be a one-off capital cost of 15.3 billion pounds to deliver the full-fibre network, on top of the 5 billion already promised by Johnson, the party said.

The Conservatives said the real cost would be over 83 billion pounds over a decade. CEO Jansen said the plan could cost 100 billion pounds. ($1 = 0.7815 pounds)

(Writing by Michael Holden and Guy Faulconbridge Additional reporting by Andrew MacAskill, Andy Bruce, Alistair Smout and Aishwarya Nair Editing by Jane Wardell and Frances Kerry)