* Elliott joins Sachem Head in push for split of businesses
* Will allow market to value businesses properly - source
* Shares up 7.5 percent on Monday after Elliott disclosure (Adds background, investor quotes)
By Maiya Keidan and Simon Jessop
April 16 (Reuters) - Hedge fund Elliott Advisors has become the second activist investor to call for Whitbread to split its hotel and coffee shop businesses after emerging as the largest shareholder in the British company.
Elliott, which disclosed a 6 percent stake in the FTSE 100-listed group at the weekend, agrees with fellow activist Sachem Head that Whitbread should split into two but differs on the best way to proceed from there.
While Sachem Head began pushing for a breakup three months ago, and possible sale of the popular Costa coffee-shop chain, Elliott is pushing for it to be listed under its own name, a source familiar with the fund's thinking told Reuters.
Whitbread shares were up 6.9 percent at 1255 GMT on Monday after Elliott disclosed the stake, which the source said the firm bought under a year ago. Whitbread declined to comment when contacted by Reuters.
Whitbread Chief Executive Alison Brittain responded to Sachem Head in January that the board continuously looked at the organisation of the group.
The Sachem Head hedge fund holds a 3.38 percent stake in Whitbread, according to Thomson Reuters Eikon data.
Whitbread has in recent years sold off its brewing business and some pubs to focus mainly on Costa, as well as Premier Inn hotels, the Beefeater restaurant brand and the Brewers Fayre pub restaurant chain.
Elliott, part of U.S. investor Paul Singer's hedge fund firm, believes splitting Whitbread into two listed entities will allow the market to value it properly, said the source.
He estimated the separate businesses would have a total market capitalisation of 10 billion pounds ($14.3 billion) from around 7.2 billion pounds now, a 38 percent increase.
The Premier Inn and restaurants business generated operating profit of 468 million pounds in 2016-17 on revenue of 1.9 billion pounds. Costa made 158 million pounds from 1.2 billion pounds of revenue.
Whitbread will publishes its latest annual results on April 25.
Elliott has started to contact banking analysts who cover Whitbread as it begins to ramp up its campaign for change at the company, according to one investor with knowledge of the matter.
Unlike Sachem Head, however, Elliott does not want Premier Inn to sell its properties. Singer's hedge fund also does not want Whitbread to take on more debt, leverage or offer further share buybacks.
Investors and analysts have long raised the idea that Whitbread should spin off Costa.
"We think the addition of Elliott as the group's largest shareholder will increase the likelihood of break-up but also believe there is much wider shareholder support for change," analysts at Credit Suisse said in a note to clients.
James Mahon, CEO and CIO at Church House Investments, which has stake in Whitbread, told Reuters: "My inclination would be to support a split... Since Alison Brittain took over in late 2015, the share price hasn't really gone anywhere."
The source familiar with Elliott's thinking said many investors wanted to invest solely in one of the two businesses.
A London-based fund manager said the reason given by the company for not breaking up before was that it believed the Costa business was not mature enough and needed the help and cashflow of the broader group to help fund its roll out.
"Clearly, as the group has grown that may no longer be the case," he said, adding that he does not own the stock, although his company is a top-40 investor,
Not all investors backed the move, however. A top-10 investor told Reuters: "Can (Costa) be run better independently of the main business? I doubt it." ($1 = 0.6994 pounds)
Reporting by Sangameswaran S in Bengaluru and Maiya Keidan and Simon Jessop in London, additional reporting by Ben Martin Editing by Peter Cooney/Keith Weir