No not one from England and Wales GRO. It would show date and place of death, name at death, sex, age at death, occupation if adult, cause of death, who the informant was, the relationship and residence, when registered,
The informant's address could well be the deceased's death and all information is only as reliable as the informant's knowledge of the deceased.
For place of birth for anyone dying in 1856 you have a couple of good choices, census returns for 1851, not so good for 1841 as only gives yes or no to whether born in the county. If they were born after July 1837 there may be a birth registration but registration was not compulsory until into the 1850s. If they were baptised you will have to check the parish registers via familysearch.org online which covers baptisms 1538-the 20th centurt but some none comformists and even some anglican churches are missing and Catholic baptisms are not as complete. You can check some county baptisms on ancestry.co.uk, particularly West Yorkshire, London and Warwickshire. Some county archives have published their parish register index, Lancashire have and I think Kent has.
If you need a search of a particular parish register it will be at the county archive/record office and most are indexed now, they can gibe a little more info than the IGI when you get into the 1900s, when residence and father's occupation started to be added by the parish.
If you would like me to check for the birth let me know the name at birth and approx year of birth and presumed location,
entering the surname Harriman into the familysearch.org database with no christian name and just a birthplace 'Scotland' and giving a date range for any event from 1790 - 1810 only brings up a few entries, mostly from the English early census returns which again does not give a precise birth place in Scotland, but none have the same surname spelling, there is a Benjamin Harriman born 1794 Leicestershire in the chelsea pensioners registers, is this a related person at all?