* CVC-Cosmen consortium proposes offering 500 pence/share
* Says 765 million pound bid will not be raised
* Stagecoach says has agreed to take NatExpress UK bus/rail
* National Express investors say happy for board to decide
* National Express shares close up 13 percent at 465.9 pence
(Adds identity of banks, updates shares)
By John Bowker and Raji Menon
LONDON, Sept 3 (Reuters) - British transport group National Express is considering an improved takeover proposal worth 765 million pounds ($1.3 billion) from a consortium led by its largest investor, sending its shares up 13 percent.
Spain's Cosmen family and CVC Capital Partners, said on Thursday they had raised an indicative cash offer for National Express to 500 pence a share from the 450 pence rejected last week.
The consortium said the proposal was final and must be recommended by the National Express board or it would be withdrawn. A formal offer must be tabled by Friday, Sept. 11 or the consortium will be forced to walk away.
A National Express spokesman said the board was considering the proposal. Its shares closed up 13.1 percent at 465.9 pence.
Institutional shareholders contacted by Reuters said they were happy for the board to decide whether to accept the revised offer.
National Express said when rejecting the previous approach it had investor support for a rights issue to repair its battered balance sheet, which sources said would be to raise 300-350 million pounds.
"It will boil down to whether the board will recommend it or not. I still think shareholders will club together to put the money up for a rights issue ... but we will leave it to them (the board)," said Andy Brough, fund manager at 3 percent shareholder Schroders.
Rival British bus and rail group Stagecoach said it had agreed in principle to buy National Express's British bus and rail operations from the consortium if its bid succeeded, but did not intend to launch its own offer.
Panmure Gordon analyst Gert Zonneveld estimated the value of British bus/rail at about 400 million pounds. National Express also owns bus operations in North America and Spain, as well as a British coach business.
A top 10 shareholder, who declined to be named, said the situation was turning into a group break-up.
"You have to be very conscious of what the sum of the value of the parts might be to the different interested parties," he said, adding the board would have to consider whether it could divide up the company itself.
Other potential suitors such as Arriva are not expected by analysts to join the fray.
ASSURANCES
The CVC-Cosmen consortium said it would fund the offer through equity provided by both the Cosmens and CVC, and had held talks with National Express banks about refinancing the group's facilities.
An industry source said the banks included National Express bookrunners HSBC, Royal Bank of Scotland, alongside BBVA in Spain.
The consortium said a pre-condition that National Express be allowed to keep two British rail franchises which are under pressure from the government had now been dropped.
Stagecoach said it had received assurances from the Department for Transport that it would not seek to take the franchises under state control in the event of an acquisition, although it would continue with its plan to take back National Express's troubled East Coast franchise.
Stagecoach shares closed up 11.5 percent at 145.9 pence.
National Express, struggling with nearly 1 billion pounds of debt, announced earlier this year it was to give up the loss-making flagship East Coast line. The franchise will go back under state control regardless of a takeover, Stagecoach said.
National Express also runs the profitable East Anglia franchise and London commuter line c2c.
It became a takeover target in June when rival FirstGroup tabled an all-share offer, which was rejected.
Arriva has said it was monitoring the situation.
Go-Ahead declined to comment on Thursday.
Citigroup is advising the consortium, while Deutsche Bank and Nomura are advising Stagecoach. Merrill Lynch and Morgan Stanley are advising National Express. (Additional reporting by Quentin Webb; Editing by Dan Lalor and Rupert Winchester) ($1 = 0.6128 pound)