The man in the lower right of the photo appears to be wearing a single breasted tunic. The tunic was authorized in 1856, but I don't believe many units received them until they returned from the Crimea. The cuffs and collars appear to be plain, or maybe are just not showing up in the photo. Decorated collar and cuffs would be an easier way to date the photo. They changed over the years.
Bit difficult to see the breeches of the weapons to tell if they are Snider-Enfield conversions used 1866 to around 1874 by the Regulars. They really do not look like Martini's, but as you stated, the photo is faded a bit faded.
Unit - Didn't notice any badges or numbers.
Maybe the photo was mislabeled? Or the men are Crimean veterans photographed on their return to UK. Possibly Militia, Volunteers or Colonials?