Hiya,
you wrote
'At the moment, I am taking him with me everywhere - loo included! - and at nap time I sit quietly with him till he settles, however I'm worried I may create a longer term problem and he won't ever gain confidence to play alone.'
I think you may be able to teach him/force him to play on his own, in the next few months. But the key part of your sentence is 'confidence'. He would be playing on his own because he had no choice, not because he were confident enough to do it.
It seems clear to me that what you really want to achieve is for him to be confident - and as a result of that, then at some point in the future, to play independently.
So, you are working on increasing his confidence, NOT on getting him to play by himself. The latter is only an effect of the former.
And to increase his confidence, you need to (pretty consistently) meet his needs - and at the moment, he needs you to be there, in his line of sight, within reach. So what you are doing sounds exactly right - and by doing that, you are NOT creating a long term problem, but rather you are doing the right thing for AVOIDING that very same long term problem.
And yes, I agree with PP - he is at the exact age where separation anxiety is the centre of everything, plus he has additional reason to be anxious about separation.
Ok as for practical ideas of how to help him... have you tried singing/constantly talking? I mean when you are leaving his line of sight. So that though he can't see you at the moment, he can at least hear you.
To get things done - use nap time? I know it is silly really but there are just times when you can't get much done.
To work on his sense of constancy - in addition to peekaboo, there are other 'games' you can play. I used to do a little song which I learned from Jolly Babies, the text is 'When my mummy plays with me, this is how she goes: She hides away so I can't see her, then she goes peepoes!' (Can't really get the tune across sorry!), but as I sang that, I'd 'hide' (just my face) behind a thin see-through scarf, then pull it away again. Eventually DS would tag the scarf away (which gives a sense of control), or I would place the scarf on his head rather than mine, etc. Thin scarfs are great for many things, very tactile, and you can usually find one in a charity shop.
Or just basic peekaboo (rather than around corners), just cover your eyes with your hands and uncover again, babies find this hilarious for some reason!
In general, speaking of hilarious, follow the giggles! My 'playful parenting' book says that LOs find it funny when something is just borderline not-quite-understood but not-quite-totally-strange either. The point they are working on, developmentally. So if you find your LO giggling at some game/action/noise/whatever, then do it again! Luckily it is usually natural and quite easy to repeat an action that makes our LOs laugh :) But good to know that you are not just making a fool of yourself for your child's amusement, but that you are helping them learn, meeting them exactly at their 'stage'.