Mounting Fog Lights on a fibreglass bumper

I put mine right on the bumper with a large washer on the back side, and have had no issues. 

Don't they jiggle a lot from road vibration if you mount them on the fiberglass bumper?

I would be more inclined to get a fog light mount that attaches to the bumper mount, instead, like this:

https://www.jbugs.com/product/...MiqJUJBoCU3oQAvD_BwE

Someone in the UK must have these, too.  Look for a mount to fit a VW bumper bracket.

The bumpers on a Chesil aren't mounted the same way. No bumper mounts. The bumpers have an extended fibreglass plate/flange that bolts to the bottom of the car. That's on mine anyway.

Well, that just sucks!  That must be why I've seen maybe ONE Chesil with fog/driving lights!

If you still want to mount the lights to the bumper then back them up with a fender washer or small 1/8" thick steel strap to give them some backing and/or put a small brace between the bottom of the light and the bottom of the bumper.

I don't have bumpers (Mine's an Outlaw) so I made my driving light mounting brackets from a 3/16" thick piece of Stainless Steel.  I now know how incredibly stiff stainless steel is.  It took a lot of heat and a really big mallet to bend them this much but they look great and fit the curves of the car.  I polished them after fabrication and they shined right up.  The lights do not vibrate at all (the mounts are super-rugged) and this approach, from the Chesils I just looked at, would work well for you, too.  You only cringe once when you drill the holes in the body, but these mounts look great when finished.  

That braided stainless steel wire sheath is a flexible water connection for a bathroom sink or toilet.  I thought it added a classy touch and the threads matched the bottom of the light stem.

I think it would be pretty simple to either fiberglass or glue a 3-4” aluminum backing plate on the inside of the bumper. Any industrial glue would be fine. I prefer Wurth Fix All.