(Talking UK here)
The ANO requires the pilot to remain at the controls (you weren't considering putting it on autopilot so you could chat up a girl in the aft galley were you?)
Apart from that in the absence of any prohibition (eg in the Pilot's Operating Handbook) I'm not aware of any reason why not.
The main issues will be that flying from the right hand seat is (for me at least) a very different experience that skews your visual references. Therefore I suggest you try it with a qualified safety pilot in the LHS so you can hand over to him if you don't like it.
The standard "keep to the right of a line feature" and "left hand circuit" are also predicated on you sitting on the left and therefore having a good view in that direction.
On my aircraft there are no brakes on the RHS and on some you might find some of the controls not replicated or more difficult to use (requiring more swapping of hands).
You'll probably also not have a full complement of instruments on the right hand side and visibility of some of the displays may be more problematic (radio right over on the left side of the panel on mine).
All aircraft are different and as a qualified pilot you are expected to be able to make your own decisions. "If in doubt don't" is usually a good fallback position. It's also good to remember that something that is legal is not necessarily sensible (and the converse is also true at times).
Perhaps UV could point us in the direction of some rule or legislation that supports his view?