I have (or rather my daughter has) a Fabuland umbrella which has been snapped off where it meets the base (probably over 30 years ago when her mum was a child).
I've seen Can I repair a broken LEGO brick with glue?, but in the best case the joint could only be as strong as the original plastic, and this is a weak spot where small hands are likely to use the pole as a lever (the base is an unusual design of slots, just visible in the BrickLink picture, and is a rather tight fit). So I thought I'd reinforce it, perhaps by gluing something like Brick, Round 2 x 2 with Axle Hole as the axle hole will also take a normal flagpole (3.18mm), but the umbrella pole is a little larger. Replacements are several pounds, and some of those are even broken in the same way.
Is there a slightly larger standard I don't know about - or would I be reduce to getting out the drill to make a reinforced version?