I just bought some 16" alloys which have 195/40/R16 tyres on them, will this cause any probles with regard to the speedo readings I get or anything else?
You just answered your own question then, if the rolling radius is different the speedo will be out and they might well clip the arches too on full lock.
Because the rolling radius is smaller that what the speedo was calibrated for it will think you are going quicker than you are.
Best thing to do is get rid of the tires and get 195/45's put on. Im in the process of looking for 195/45 R16's now for my 500 alloys
If you dont fancy doing that you can also get your speedo re-calibrated. the cheapest way of doing it is driving with a satnav with speed indication or go past on of those Street signs which show your speed. that will show you the percentage that your speed is out to the indicated speed
You just answered your own question then, if the rolling radius is different the speedo will be out and they might well clip the arches too on full lock.