My suggestion would be to approach your local Glass/Glazing shop and give them the exact dimensions of the circle and the hole . Thye will be able to cut this out of some properly tempered or reinforced glass and polish it up for you and make the edges neat . All told it should be less that 50/60 quid and will fit to exactly what you want . Most shops would have offcuts that would be suitable for the blank so reduce the cost as there is not much else they could use them for . Not sure what is around you locally but try a couple of places as with all shops they can differ quite a lot in how they respond , costs and being helpful I found a great one near by and he has helped with a number of glass ideas I had for not much money . In one instance he was so taken with the idea and what he needed to do that he only charged me a nominal sum for his time no material costs.