I don't think there will be emigration records from the UK for that date, but I have found this on the US immigration records:
https://www.ancestry.co.uk/interacti...=successSource
New York, Passenger and Crew Lists
arrival New York 5 Jul 1842 on the "Normandie" from Liverpool
William Grimshaw 26 Male Farmer origin Ireland, destination New York
John Stewart 24 dittos
Margeret Grimshaw 20 Female Wife Do Do.