A 50cm*50cm 5mm thick sheet of HDPE is 8 quid from Directplastics. How would you cut the 20mm stuff down? I can't think of any half accurate way with hand tools. Potentially very material-inefficient, too, assuming it could be done at all; the cost of material lost in doing it is probably about the same as the cost of some 5mm sheet.

If you can get some stainless sheet, even 1mm thick will make for a sturdier base than 5mm HDPE. Of course, it is harder to work. If you have a hacksaw, patience, and suitable drill bits you're there.

A source of thin steel in huge amounts often for free is kitchen white goods.