The Three Arrows was at No.257 Deansgate according to the 1825 street census, was still there in the 1861 census. It's shown on the right in this Archive photo from 1872. The Three Arrows probably made way for the Great Northern Warehouse which was built at the end of the 18th century, as No.257 Deansgate these days is King Sturge property management, near to the main Deansgate entrance to the Great Northern.
257 Deansgate. (c) googlemaps.