So, Jen and I are just putting some new vinyl flooring down in the bathroom. Unfortunately, we've obviously jogged the toilet pan, because there's a minor leak.

It's coming from where the outlet of the pan mates with the waste pipe. There's the remains of some kind of rubber sealant there. I'd like to know what kind of sealant I need to replace it with. Will the stuff that you use around the edge of the bath do, or do I need something different?

While we're on the subject: what should I do about gaps around the edge of the vinyl? I seem to recall some kind of waterproof self-adhesive edging tape that's V-shaped: you put one leg of the V a little way up onto the wall, and the other leg onto the vinyl. This hides the gap, and seals it properly. Did I make this up, or does it exist?

Toilets are typically sealed to the floor with a parafin ring.
It's a one-time use thing: smoosh.
Plumbing store or hardware store is your best best.

I have seen ones like that in the USA but only in public restrooms.

I'm not sure that you can use silicone mastic for a permanent fix: it is a non-bonding sealant, so it will peel off after a while. It doesn't really live well with urea (pee).

The ideal would be a tube of Acrylic sealing mastic, that dries semi-flexible. Even better would be a cyanate-based waterproof toilet sealing mastic (light grey, semi-setting) but this is a bit more expensive and poisonous if you don't handle it properly (good ventilation, plastic/rubber gloves). I would still recommend it as the best repair, though. B & Q should have it.