Hello Again,
If he was 50 in 1861 he would be born Abt. 1811 - the chap in the 1861 census for the Impregable was born Abt. 1820.
There is a William Andrews born Abt. 1811 on the HMS Wellington (RG9; Piece: 4493; Folio: 57; Page: 12; GSU roll: 543293)
His is described as "able seaman" It would be very unusual for a rigger to become a Coxswain (especially an Admirals Coxswain). Could this be him? - It is stated he was born in Portsmouth, im not sure if that fits.
I live in Portsmouth and the City Museum has a massive naval history section. If you think this is him I can do some digging when i'm over there next if you like.
Cheers
T