There's a model shop near me (Stoneleigh, Surrey) which sells small
bottles of plastic weld fluid, which sticks many types including
Perspex. You position the two bits you want to join together, and
apply this very thin liquid to the join so that it wicks into the gap.
It works well, and presumably is available in other parts of the
country. It says it contains Methyl Chloride. I didn't have to sign
anything.

Dave W