Thanks for the replies everyone.
I am referring to a Beogram 2200 (thanks Craig) and a Beogram 1902 which both have the same problem. I tried superglue without success on the 1902 but it might be worth another go.
The IPS WELD-ON #16 Cement for Acrylic Sheet sounds like what I need, bit I can only find US Suppliers and they are unable to supply internationally for legal reasons ( I think because it's highly flammable). Does anyone know of an equivalent product that is available in the UK?
Simon