Matt,
Saying "it's a burner" is all well and good but that's like smacking a drawing pin with a road drill! It's like telling you to replace an entire car engine when only one part is causing the breakdown.
It could be one of several parts on that burner that's causing you a problem - or it may not even be the burner at all, we could be looking at a problem with the oil line - maybe blocked filter, or perhaps even at this temperature the oil itself is "waxing" (freezing).
Do yourself a favour, get an OFTEC registered engineer to check the boiler over cos it will be a lot cheaper than a new burner. It's really not something you want to tackle yourself.
Bunslinger
January 2010