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You have my commiserations.  I fear all the modern ones slip about, or that's been my experience, at least.  I've tried super light plastic ones, a heavy resin one, and a wooden seat with brass fittings.  They they all slide even with special rubber packing washers!  It's maddening, isn't it?  I've tried those sticky pads that sit over the screw holes and regret it as now the pads are stuck fast and the current loo seat started to slide sideways after a few weeks.  I'm all ears if anyone can recommend a good seat.  The only thing that's helped has been to relocate the loo roll holder so that grabbing the paper doesn't involve twisting.  You are far from alone with this problem.  What I don't understand is how this situation came about.  I don't recall this being such a widespread problem until the last few years.  Did all the manufacturers get together and agree to redesign their production lines to fail?  After all, if they're all terrible once one discards the tired but servuceable seat one becomes committed to buying a new one every few months until it dawns that they're all rubbish. 

it slips sideways?  that suggests the attaching nuts and screws aren't too good.  might be they can be readily replaced at the same store where you got the new seat -- grampa