Who ever you get to fix it, make sure they are Gas Safe registered, you can check there reg number is legit here http://www.gassaferegister.co.uk/
1) The pilot flame is too small to heat the thermocouple.
2) The thermocouple is duff.
3) Something else - like an overheat stat - needs resetting.
4) The gas valve is faulty.
Let's hope it's not the last one!
I include the following information just in case you're interested because somebody will surely [censored] me off if I try to tell you how to fix your own boiler ---
Most flame failure devices work the same way. You press the button in to get gas to your pilot jet and light it. The thermocouple heats up and generates a tiny voltage, just enough to energize an equally tiny electromagnet inside the valve. This holds the valve open after you take your finger off the button.
An overheat thermostat may be wired in series with the thermocouple. If it operates it cuts the power to that magnet and the valve shuts, just as if the flame had gone out.