The out-of-gamut warning just means that the internally developed image has colors that exceed the color space specified for the softproof. You are using a monitor that has approximately the gamut of sRGB, so the image will look approximately like it is supposed to be when converted into the sRGB color space on export. However, if you would use a wide-gamut monitor, you would see that the image areas where the softproof indicates out-of-gamut for sRGB are looking more saturated than on the sRGB monitor.

This is perfectly normal. LR does not let you choose a working color space. Instead, it internally uses a very big theoretical color space (size of ProPhotoRGB) and will always use the maximum gamut available by your monitor for display.

OK, so let me explain my issue:

• I start with an sRGB image.  One would imagine that an sRGB image doesn't have colours outside sRGB?
• So why does Lightroom report out of gamut colours when I proof against sRGB?

Perhaps you increased the saturation in the development module? The color space of an imported image does not matter. When developed, it is always converted into the huge internal color space.

Otherwise, if saturation was not changed, then there really should not be any out-of-gamut warning.

EDIT: I just tried it: Imported an sRGB JPEG into LR and made a softproof on sRGB. A few small areas in the image are reported in the out-of-gamut warning, which is not logical. I suspect that the warning appears on colors that are just on the edge of the color space, so a sRGB image with extremely satuated colors could just trigger the warnings.

Here's an image with an embedded sRGB profile:  http://www.simongarrett.co.uk/Primaries_sRGB.tif

It contains colour blobs of 100% saturated colour - in sRGB.  Imported into LR, and with no editing whatever or develop presets applied, it shows out-of-gamut colours when soft proofing against sRGB is applied. 

Was the image you exported to your desktop as JPG from the original RAW or from the re-imported web-module image?

CSS Simon wrote:

 

OK, so let me explain my issue:

• I start with an sRGB image.  One would imagine that an sRGB image doesn't have colours outside sRGB?
• So why does Lightroom report out of gamut colours when I proof against sRGB?

It’s a bug IMHO. You’ll see the same bug in Photoshop! I’ve written to some of the color gods within Adobe but haven’t heard back. Bottom line, the OOG overlay isn’t useful in the first place but it should be accurate. That is, if you soft proof an sRGB image with sRGB, you should see zero OOG colors. That isn’t happening. Best ignore OOG anyway. It has always treated 1% and 100% OOG the same with an ugly overlay that blocks your image. And what are you supposed to do anyway? Manually desatruate to remove? Nope, not a good idea. The output profile will do this faster and with more precision, especially if you prefer the visual appearance from a Perceptual rendering which alters in and out of gamut colors.

Where OOG could be useful is when editing your master when not being careful with sliders like Vibrance or Saturation. The data is in a very wide gamut space using ProPhoto primaries. Even with a wide gamut display, there are colors you can alter you can’t see. Having OOG pop up as an option in such a case could be useful: warning Will Robinson, don’t move that slider so far! Short of that, the OOG overlay, which predates ICC color management in Photoshop where soft proofing was an option isn’t useful.