I think you need to drive at a decent speed on 'fast' road for 20 minutes or so for the rest to happen, so the system has time to calibrate. At least that was what my HRV had to do.
If you actually have tyre pressure monitoring valves, the reset should be pretty much instant. In this case, if the light won't go out, then you may have a faulty valve or the battery has expired. Good luck figuring out which one it is though.
On my Toyota, they wanted over £200 for a replacement valve. My local tyre shop replaced with a compatible version for a fraction of that. They may also have a way of figuring out which one is faulty.
As far as I know, if the fault light is on your car will not pass the MOT.