I have had this and what a fiasco. My burner 2 years old on Sunday (the date is marked on it) - turns out (i) the photocell was kaput.....could be your problem if oil - my burner igniting but not continuing, the button going back to reset after a couple of minutes.
the second problem turned out to be the ignition assembly - but then the CO reading was 4000ppm.....somewhat high. This afternoon, they replaced it (£78 for the part) and it could all have been redundant as the guy who did it said we had a CO problem, the same reading, and no idea that this was identified on Monday...... A phone in, 'we can't send a senior engineer out to Tuesday' - a rant about Saturday and o-time and she comes back that they'll send someone out this afternoon....took him 30 seconds, he removes the eye tube that ups the air in and oomph up she goes and the CO level comes down to 21ppm.
The boiler is ancient - he takes the measurement of the top plate and they'll make a new one and then come and drill the rusted bolts out and clean the carbon out of the boiler...... The heat is now coming in - just as things are supposed to warm up this w/end.