Since it's in the bathroom and it's red, it could be mold.

Have you used any bleach cleaner on this and does it disappear for a while?

I don't recognize quite that pattern, but if in your bathroom and becoming worse, I'm going to say it has to somehow be water related. You've got a leak or intrusion someplace.

I'm not sure what the substrate is - probably plywood? We haven't used bleach, I don't think, but we've used various cleaners and vinegar and nothing comes off, it doesn't touch it at all.

We are getting the bathroom renovated soon (it needs it!!) but I'm wondering how big a problem it could be...

It can be a big problem, if the subfloor and even the joist are going rotten from the moisture. If this is on the second floor, then you could end up with damage to the ceiling below as well.

Don't wait for your reno, look for the leak and fix it now.

ETA - bleach or any other cleaner used on the top side of the vinyl won't do anything. The stain is coming from underneath, where they won't penetrate.

Thank you all - I'm getting someone in to look at it. I'm pretty sure i know how the water would be getting in there so I can at least stop that for now!