* QIA, Brookfield make 350 pence-per-share cash offer
* New offer values Songbird at 2.6 bln stg
* Songbird has said it is worth 2.8 bln stg
* Comes amid revival in London office property market (Adds Breakingviews)
By Clare Hutchison
LONDON, Dec 4 (Reuters) - Qatar's sovereign wealth fund and a North American investor have upped their joint bid for Songbird Estates, the owner of London's Canary Wharf financial district, with an offer that values the company at 2.6 billion pounds ($4.1 billion).
Songbird is the majority owner of the Canary Wharf estate, established about 25 years ago on former docks as a new financial zone. It is also a part owner of the landmark "Walkie Talkie" skyscraper in the City, London's traditional business area.
It rejected an initial 2.2 billion-pound approach from the Qatar Investment Authority (QIA) and Brookfield Property Partners, saying it significantly undervalued the group. Last week, Songbird said it was worth 2.82 billion pounds thanks to an upturn in property markets.
In a hostile move, the QIA and Brookfield took its new all-cash offer of 350 pence per share directly to shareholders.
Announced less than two hours before a deadline to submit revised bids, it represents a 33.6 percent premium to Songbird's closing share price on Nov. 5 - the day the first approach was made.
"The Songbird offer provides an attractive opportunity for Songbird shareholders to realise, in cash at a premium, their investment in a highly illiquid stock which has not paid a dividend over the past five years," the two companies said on Thursday, adding the offer was final and could not be increased.
The QIA already owns 28.6 percent of Songbird, while U.S.-listed Brookfield, which operates and invests in office and industrial property, has a 22 percent stake in Canary Wharf Group.
Songbird declined to comment on the new bid.
Analysts have long expected a takeover of Songbird to simplify its complicated structure - it currently has two layers of shareholders, one in Songbird and another in Canary Wharf Group. It shares have tended to trade at a discount to its net asset value because of its set-up.
A revival in the London office property market and Canary Wharf's pipeline may have also stirred interest.
Canary Wharf is preparing to start work on two major new additions - a 60-storey tower that will contain the first residential property on the estate and a new 20-acre waterside site providing 3,100 homes and office buildings, as well as a school and more retail space.
A successful bid would add to Qatar's already significant presence in London. The Shard, western Europe's tallest skyscraper, and department store Harrods are among its high-profile properties.
Any deal would have to gain the approval of Songbird's other major shareholders, including New York-based investor Simon Glick, who has almost 26 percent, and China's sovereign wealth fund, which owns 15.8 percent.
Glick did not immediately respond to a request for comment. The China Investment Corporation could not immediately be reached for comment.
The QIA and Brookfield said top 10 investor Third Avenue Management had accepted the offer at the new price.
Another significant shareholder in Songbird told Reuters ahead of the revised bid that it any new bid should be at least 400 pence per share.
Songbird shares closed down 1.1 percent at 328.5 pence.
In a separate statement on Thursday, Brookfield - part of Canada's Brookfield Asset Management - announced that the QIA had bought a 9 percent stake in it.
1 US dollar = 0.6379 British pound Additional reporting by Carolyn Cohn and Anjuli Davies; Editing by Sophie Sassard and Pravin Char