UPDATE 1-Madison backs Qatari bid for Canary Wharf owner Songbird

(Corrects third paragraph to show offer to shareholders followed rejection of initial bid; removes reference to hostile bid)

* Madison holds 12 pct of Songbird free float

* 28 pct of free float shareholders back deal - QIA

* Follows $4 bln bid last week

By Simon Jessop

LONDON, Dec 8 (Reuters) - Songbird Estates shareholder Madison International Realty plans to accept Qatar Investment Authority's (QIA) offer for the British property company, the sovereign wealth fund behind the hostile move said.

The offer of 350 pence per share for the owner of London's Canary Wharf financial district was launched to Songbird shareholders by QIA and U.S. investor Brookfield Property Partners (Other OTC: PGPHF - news) on Thursday.

The hostile move followed Songbird's rejection of an initial 2.2 billion pound ($3.43 billion) approach, saying it did not reflect the full value of the company or its growth potential. Songbird has yet to formally reject the improved terms.

In a statement on Monday QIA said that Madison had written a letter to Songbird saying it intended to accept the offer before its closing date.

Madison holds a total of 18,627,054 Songbird shares, representing approximately 12 percent of Songbird's shares in free float and 2.5 percent of Songbird's issued ordinary share capital.

Taken together with backing from fellow shareholder Third Avenue Management, QIA has so far received public support from holders of about 28 percent of Songbird's free float, it said.

Shares (Frankfurt: DI6.F - news) in Songbird were up 0.6 percent in early deals on Monday, outperforming a 0.4 percent lower FTSE All Share index . ($1 = 0.6420 British Pounds) (Editing by David Goodman)