First things first, don't poke at it!
I don't think it will be testable there as it not within 30cms of a suspension or seatbelt mount, so you should be safe for MOT... I think that section is just a reinforcer for the boot floor. However, it looks very crusty indeed, and the front of the spare wheel well doesn't look too sexy either. I can see why it was commented on.
Any holes through into the boot floor, and you are going to start running into problems with the tester's discretion. Have a look in the boot under the spare wheel, but please don't poke at anything that looks scabby.
As for what to do with it, you have a few choices, and it depends how rotten it is. You need to have a very careful look to see if you can determine the extent of the rot. You can either clean it up very carefully, fill it with waxoyl & underseal it and nurse it for as long as you can, or you can explore the extent of the rot - but be prepared for some significant welding (and expense). You might also want to have a look at the inner sills and around the front subframe mounts, but again, don't poke at anything that looks suspicious.
Whatever you do, be gentle with it for now. It's not structural, so you could do a cover up job if it's reasonable and you can arrest the rot. It may not be as bad as it looks, but it's hard to tell without actually seeing it with the eyeballs.
It's a bit of a bummer when you find stuff like this, but it's not the end of the world. Where has the car come from, has it been a seaside car?
