I found this book online which is quite interesting ‘The Watering Places of Great Britain and Fashionable Directory’:
https://babel.hathitrust.org/cgi/pt?id=uc1.31822035072578;view=1up;seq=103Jump to page 87 where it starts discussing Bognor and there are mentions of the Earl of Arran including this on page 90:
SUDLEY MEWS – The want of this description of accommodation has long been complained of by families who have visited the different watering places. In Bognor, however, they have more than emulated the metropolis, for Sudley Mews are not only most spacious, but in their economy, most complete. There are accommodations for horses and carriages of the most superior and extensive description, and also sleeping rooms, and a general sitting room for coachmen and grooms, with an area sufficiently extensive for the exercise of a regiment of horse, with a pump of excellent water in the centre. They were built by Mr Pearson, the present proprietor, who is likewise the worthy steward of an equally worthy master – the Earl of Arran.