I personally consider the guage very important.  The sensor that feeds
it isn't telling anything else what the temp of the coolant is, just
you.  So, technically, it's not 'important' to the running of the
engine.  But I certainly want to know if I'm running hot or cold.

I had mine replaced last spring and the sensor was just under $20 USD. 
Assuming prices are relatively cheap in the UK, I wouldn't think twice
about replacing it.

As to whether it's the thermostat or the sensor, I don't know.  If the
engine appears to be sufficiently warm, and you're getting good heat
out, and the front radiator gets good and warm, I'd think it was the
sensor.  If things do appear to be actually cool, it's probably the
thermostat.

Concerning the red light, it should blink when you start up the engine
for a few seconds.  This is a test to let you know the bulb works.  If
it's not even doing that, then there is something wrong with it.  Most
likely, the wiring has a break in it, or there is corrosion at the
connectors.  I say this because LEDs aren't known to 'burn out'.  Of
course, I'm just assuming that it's an LED!  You definately want to make
sure that it works!

Good Luck!
Tonya
87 Vanagon GL Wolfs
74 S. Beetle