LONDON (Reuters) - CityFibre agreed a 538 million pounds takeover by a Goldman Sachs-backed consortium on Tuesday, saying it will be easier to fund its plan to build full-fibre networks serving 20 percent of the UK market under private ownership.

The consortium, jointly owned by Goldman Sachs' West Street Infrastructure Partners and private equity firm Antin, will pay 81 pence a share, a 93 percent premium to Monday's closing price of 42 pence, CityFibre said.

CityFibre, which listed in 2014, is building its own fibre-optic broadband network in Britain, taking on national provider BT in selected towns and cities.

It signed a partnership last year with Vodafone that will see the mobile company market its ultra fast broadband networks in around 12 British towns and cities, starting with Milton Keynes, Aberdeen and Peterborough.

Infrastructure funds are targeting opportunities to invest in Britain's communications networks, which the government wants to upgrade to "gold standard" fibre connections.

M&G Prudential tied up with broadband provider TalkTalk in February to build a network connecting 3 million British homes and businesses, with an equity investment of up to 500 million pounds and borrowing of around 1 billion pounds.

CityFibre's chairman Chris Stone said the Goldman Sachs deal would provide long-term funding.

"Under private ownership, CityFibre will be able to gain alternative and potentially easier access to the financing required for its announced FTTH (fibre-to-the-home) deployment," he said.

"This will strengthen the company's ability to deliver on its vision to provide full fibre infrastructure to 20 percent of the UK market."

The buyers both said they wanted to support CityFibre's vision to extend fibre-based broadband networks across Britain.

CityFibre's shares jumped 89 percent to 79.2 pence a share after the offer, which is backed by 68 percent of existing shareholders, was announced on Tuesday.

Analysts at Macquarie, who rate the company "outperform", said CityFibre was at the vanguard of FTTH in Britain, but the project was in its infancy and the potential was significant.

"The offer price of 81 pence (...) is attractive reflecting the early stage of the business, but is well below our long-term target of 150p and significantly undervalues the business in the long term we believe," they said.

CityFibre's Chief Executive Greg Mesch said the company had raised 325 million pounds as a listed group, but it was now looking for long-term capital.

"We think it's a perfect time to shift from public ownership and public scrutiny to private long-term patient capital while we go through this mass period of construction," he said.

Its ambitions extend to 5 million premises, which based on average build costs of 500 pounds per premises, would require investment of up to 2.5 billion pounds.

CityFibre also said on Tuesday that its turnover more than doubled last year to 34.8 million pounds, helped by the acquisition of wholesale fibre company Entanet.

Adjusted core earnings for the year to end-December rose to 4.5 million pounds from 2.5 million pounds in 2016, it said.

(Editing by James Davey and Alexandra Hudson)

By Paul Sandle