Today Nathaniel says:
"The New Metropolitan Theatre is to be forthwith erected on a plot of ground on the east side of Leicester Square, formerly the site of Jaunay’s Hotel". The name Jaunay originates from France. François Marie Jaunay fled the Revolution and established Jaunay's Hotel in Leicester Square London on the site of the Odeon Theatre just around the corner from St Martins In the Field.
The Odeon was built in 1937 on the site of the Alhambra Theatre, a large music hall dating from the 1850s.
The Alhambra was a popular theatre and music hall located on the east side of Leicester Square. It was built originally as The Royal Panopticon of Science and Arts opening on 18 March 1854. It was closed after two years and reopened as the Alhambra. The building was demolished in 1936.
A bit more, but no mention of The New Metropolitan or any buildings on the site as early as 1846:
The Leicester Square theatre's name was changed frequently, but usually reflected the building's (very loose) stylistic associations with the celebrated Alhambra in Granada, Spain. By 1864, the circus had become the Alhambra Music Hall. Rebuildings occurred in 1866 and 1881, by Perry and Reed. From 1871, when it obtained a licence, an equestrian ballet was performed. The Alhambra was destroyed by fire in 1882, and was rebuilt in a more restrained style by Reed, reopening in 1884 as the Alhambra Theatre. Further rebuildings were in 1888 by Edward Clark, 1892 by Clark and Pollard, 1897 by W. M. Bruton, and in 1912 by the prolific theatre architect, Frank Matcham. Other names used during the life of the theatre were the Royal Alhambra Palace; Alhambra Theatre of Varieties; Theatre Royal, Alhambra; Great United States Circus and New Alhambra Theatre.http://www.oldlondonmaps.com/stanfordpages/westminster03b.htmlAbout 2 streets below the red "I" is Leicester Square, and on the right side of that The Alhambra is marked.