A faulty thermostat will not cause the emission problems you have; in any case the MOT test requires the engine to be at "normal operating temperature" when tested; the tester will either leave it running to warm up, or will sit with his foot on the accelerator for a bit...
The lambda probe starts working a few minutes after start-up, and has its own internal heating element to get it up to temperature.
If the engine is in good condition and everything is working as it should, even with the cat removed, the CO should not be more than about 0.6%.
The most common causes for the levels of emissions you're talking about are lambda probe and AirFlowMeter. However, if the car has been running like this for any length of time, there will be a lot of soot built up in the cat, so once the problem has been rectified, the car will need "a good thrashing" to clean the cat out.
As someone else said, bosch or OE for the lambda sensor, same applies for the AFM if required.
GTV handbrakes are notoriously bad; change the discs if they look at all suspect (look at the inside surface) and examine the cables for signs of deterioration (particularly where they are clipped to the spring pan).
And change your thermostat!
Hope that helps, Good Luck!