Great work you did on the Nest Thermostat. Quite funny to see that people in Europe (the Netherlands) were working on it to get the Us version to get work on their European systems.
You could have save you a lot of troubles and time if you simply bought an UK/EU version of the Nest Thermsostat. This one comes with a so called 'Heatlink' which is basicly a very smart 24 V relay. https://nest.com/uk/support/article/What-is-Heat-Link
Keep up the good work!