Sandell, which owns just over 3 percent of the struggling company, wrote to the directors of FirstGroup to urge them to spin off and float the U.S. unit which includes the yellow school buses that operate across 38 states in the United States.

It also called for the group to sell the iconic Greyhound bus service, which transports 18 million passengers across America each year.

A spin off and disposal of the U.S. assets could appeal to yield-hungry North American shareholders and to industry buyers due to its strong brand and cash-flow generation, the investor said, enabling the group to invest in its British bus business and bid in future rail franchises.

"Our established track record in company analysis and our sector expertise tells us that FirstGroup can turn around its historic poor performance by focusing on its UK Rail and Bus businesses," Chief Executive Tom Sandell said in a statement.

FirstGroup rejected the proposal, saying it contained structural flaws and inaccuracies.

The high-profile attack caps a torrid year for the leading transport operator in Britain and North America, after it launched a discounted rights issue to raise 615 million pounds to pay down debt and avoid its credit rating turning to junk.

FirstGroup has struggled to reduce its borrowings, much of which were incurred by the 1.9 billion pound acquisition of U.S. bus business Laidlaw in 2007. It was also hit last year by the loss of a lucrative deal to run Britain's West Coast Main Line when the government found flaws in the bidding process.

Shares in the Scottish group, which transports more than 2.5 billion passengers every year, have fallen 75 percent since the Laidlaw deal in February 2007.

The group had said at the time of the acquisition that it would consider selling off the Greyhound service.

Despite the challenges, FirstGroup said it still believed its current multi-year program, with its objectives to improve growth and return cash, would in the long run offer superior value for shareholders compared to alternative proposals, which it had considered.

Shares in the group were up 2.6 percent in early trading on Wednesday, valuing it at 1.4 billion pounds.

Liberum analyst Gerald Khoo said in a note to clients that he also struggled to see the merits of the Sandell proposal, and that investors would have to remain patient if they were to see value realized at the group.

"Selling underperforming assets when they are cyclically depressed is unlikely to realize more value than restructuring them, and seeking an exit at a better point in the cycle, if appropriate," he said.

"Both businesses are leaders in their respective markets by substantial margins (both are a multiple of the size of their nearest competitors), so the synergy opportunities available to trade buyers are limited, in our view."

Shares in FirstGroup have fallen 23 percent in the last 12 months, including a sharp drop in May when the group cut its final dividend. Its performance stands in stark contrast to rival Stagecoach which released an upbeat market update on Wednesday.

(Editing by Tom Pfeiffer)

By Kate Holton