The J.T. Haden photographers at 185 Broad Street, Birmingham were established in 1854 and appear to have still been there c1880. Later they moved to 255 Broad Street and also started to add year pictures were taken on the back; see
http://earlyphotographers.blogspot.co.uk/2011/07/haden.html and
http://www.rogerco.pwp.blueyonder.co.uk/list120/lambert.htm (scroll down (or click Edit find “broad street”) at least 3 images)
I don’t recognise the uniform as British, if it was then I would have said light infantry, but there are some conflicts: there’s a distinct bugle identifiable on the cap badge, typical of Light Infantry (would also feature on US Infantry badge) but I don’t know of a light infantry kepi style cap with a feather; the cross-belt with badge is similar to light infantry, but the chain and whistle are missing. Another point is that no British soldier would normally be pictured in a studio photograph with a firearm; add those two together with a British studio and it’s probably a costume.
Some photographers to offered theatrical costumes for customers to dress up in and some still do that today for tourists.
If is a US Civil War Infantry uniform (costume or not) just in case someone else can identify it I’ve cropped the picture from the background. If you don’t have a program to do that, download IrfanView it’s free.