Could be that you have condensed water in your fuel line.
The oil itself should only freeze at extreme temperatures.
We have had a similar problem this morning. This has happened to us before during prolonged cold weather and our engineer explained the cause as above and created a lock out on our boiler.
Our boiler and feed line get no sun all day and are quite exposed
If you can, clean the filter near your tank. Possibly frozen water or contaminants are to blame. Also consider lagging your feed pipe from the tank to your boiler - I will be doing this when I get home from work!
Hope the line has thawed out by then...quickly wrapped some foam underlay around the pies this morning at 06:00!
If none of this works you will need to get a professional in I'm afraid! Good luck.
Darren - Great Bardfield, Essex, January 2010