Its intervention comes almost three months after Reuters reported that another activist investor, Sachem Head, wanted Whitbread's management to examine a breakup as a way to boost the value of its individual businesses.
Investors and analysts have long raised the idea that Whitbread should spin off its popular Costa coffee-shop chain.
Shares in Whitbread soared by 6.6 per cent after Elliott, the U.S. hedge fund, confirmed that it has become the largest shareholder in the company.
A spokeswoman for Whitbread has declined to comment.
According to reports, Elliott Advisors wants Whitbread to be split into its Costa Coffee chain and its Premier Inn business.
"He told the Today programme: "[Elliott] don't necessarily want the properties to be sold the way that more aggressive activists do, they just want two separate companies so they can value hotels alongside, say Hilton, and Costa alongside say the likes of Greggs and they think that will create shareholder value".
Whitbread https://www.whitbread.co.uk/investors shares rose 6.5 percent by 1030 GMT on Monday after Elliott disclosed the stake.
City analysts have also been piling the pressure on Whitbread to take a decision on Costa in recent months.