There is no logical reason for insisting that "alright" is incorrect and should always be written as "all right", when other single-word forms such as "altogether" have long been accepted. The fact that "alright" is not recorded until the end of the 19th century, while other similar merged spelling such as "altogether" and "already" date from much earlier, is no reason for denouncing it, but many people still find it unacceptable in formal writing.
(Oxford A-Z of English Usage - Jeremy Butterfield)
(Oxford A-Z of English Usage - Jeremy Butterfield)