Can find no reference to J.Harrison ,Strand, London, Possibility exists that the gun was made at some other location and given a fictitious address.[I once owned a gun marked J.Manton,Strand,London, fake of course!]
At least Two J.Harrisons are listed as active in the English trade they are:
J.Harrison,[1857-1861]Gun stocker,9 Lancaster street, Birmingham.Despite being listed as a stocker, it is quite likely that he finished and sold guns bearing his name.
James Harrison[1847-1857]Driffield and Leeds, Yorkshire.Business appears to predate the gun you describe.