Can't find any detail on R. Mitchell artist, Portsmouth painting

It looks like a good amateur to me.  Why not contact the pub, they may know.

It will almost certainly be an original watercolour (unlikely this would have gone into print), and by an amateur hand. The drawing looks reasonably proficient but the painting lacks tonal depth, in fact there isn’t any tonal depth, which is why it looks ‘flat’. Undated, but the edge of the bevel is discoloured which tells me it could have a bit of age… a fair few decades at least! There’s thousands of unlisted amateur artists out there, so the chances of finding any information on this particular R Mitchell is remote at best!

I agree it's an amateur's painting - or shall we call it a non-professional's painting, because Mr or Ms Mitchell was no ham-fisted first-timer.  It's meticulously done - every detail caught - but painted either from a photograph or in the most unflattering possible light: the artist's aim was to capture the detail, and they did.  The play of light and shadow - i.e. tonal contrast - was unfortunately of no importance to them. But - that doesn't make the painting any less of a desirable thing to hang on your wall: someone worked hard on this to the best of their ability at the time, and caught a scene as it was, without much by way of embellishment.  I doubt that R Mitchell is a known artist - as Sylvia suggested, ask at the pub, ask older residents of the area: you might even find R Mitchell in person!