That is ridiculous.Took it to a garage close to me and was quoted around £200
I had my Golf GTI thermostat changed and that was connected to the cam belt right at the bottom of the engine.
I got it done for £120 incl part. Think you need to try another garage.
Try the OBD reader as suggested.
Also. Did you drill a hole in the thermostat?
I’m assuming you followed a guide online?