This light appeared on my car about a week ago... I checked the pressures when I got home. They were all within 1-2 psi except one of the back tyres which was about 3psi down. I topped them up, reset it and it's not been on since. My front tyres are down to about 3mm of tread... Am I right in thinking that the computer uses data from the ABS sensors to detect differences in wheel diameter?
Yes. On the Golf, the TPMS doesn't measure the actual pressure, but merely looks for differences in rotational speeds. It uses some kind of fuzzy logic to allow for gradual tyre wear, so, if you have brand new boots on the rear with 7½mm tread, and the fronts are on the TWI at 1.6mm - it will still work. However, if you were then to swap those wheels front to rear, then it would ping the TPMS warning.
One downside of this system (compared to actuall pressure sensors, like in my RS4), is that it can take 20 minutes to register a puncture - pretty pants if you ask me!
I've read somewhere that this data is also used by the sat nav to calculate position when the satellite signal is lost momentarily. (Dead reckoning)
Yup. All factory fitted SatNav systems use this data, unlike all dash mounted stand-alone, and many aftermarket replacement head units. It works very well too. On my "european tour" in my RS4 last May, I went through a long tunnel (near a resevoir in Switzerland, going towards Austria) - seemed like 15minutes underground - and the SatNav screen displayed exactly where I was on the map!