Wet weather is ideal for slugs and snails. Other grubs? Prbably the cabbage white butterfly grub if it was hidden in the broccoli. I think you have to accept these occasionally. I don't think it's possible to eliminate all pests. An if you did manage to do so, their natural predators would leave, leaving you wide open for a concerted attack. Sorry I haven't been of more help. My Nan grew veggies, we're talking 1950s here, and picking out slugs, grubs and other assorted greeblies was just the way it was.

To get grubs out of broccolli and other vegies, soak in iced water after picking. Apparently the grubs float to the surface.

So far this year we have been lucky with grubs and haven't noticed any but last year I grew a huge broccolli and was really looking forward to eating it, but when I cut it up I found the whole inside was eaten out but there was no sign on the outside. I was very disappointed :(

There are lots of hints for detering the cabbage moth, some may work, some not. Just browse organic growing for lots of hints.

Stopped growing Broccoli for this very reason. Besides more tomato space was needed:-)
The iced water idea sounds good.

I use salt water in the same way. They just float and die, it's bliss to watch.

Your conditions would be similar to mine in North West Tas. I only grow Broccoli as an autumn to winter crop, planting after the cabbage moth has gone to god. I also try to grow a quick crop by feeding them well. Apart for Attilla the Snail, there is no worse enemy than the Cabbage Moth. I suggest you use Dipel. This will kill any of the little caterpillars in a biological friendly way. You need to reapply a few times after rain, but if you get the caterpillars before they turn into moths, you will have fewer infestations because the now none existent moths can't lay eggs. It's a bit of a Catch22 situation, but if you can break the life cycle, you are ahead. Onlt when you no longer see the Moths dancing to taunt you, will you know you have succeeded! Slugs and snails are a fact of life - I think I've just got Atilla and his marauding hordes under control and one rain and they're back. One even crept into the hothouse - he didn't last long. I use organic snail bait and now that I have a beaut new capucchino machine, will put the spend coffee grounds around individual plants. The residual caffeine is supposed to kills smails and slugs. I soak my produce in salt water and have been generally successful in only getting a few - they will come out gasping. Companion plant nasturtiums. Good luck! Adam - you have a sadistic streak like me eh eh?
Cosmic