Hi DizzyDi
Did your team not give you any help moving from Insulatard to Levemir?!? That's terrible! They are very different insulins, and you should have been given quite a bit of help and support in making the transition.
Do you have access to a specialist DSN who you could ask for advice?
I'm only going on what I hear from Levemir users as I'm on Lantus (though I am considering talking to my team about switching)...
From what I know (it's a long time since I was on it) Insulatard is a medium-long acting human insulin with a fairly short onset, something like half an hour, followed by a peak activity until about 12 hours after injection, then a gradual tail off up to 24 hours-ish. I took mine in one dose, late at night and ate a little supper to counteract the overnight peak.
Levemir on the other hand is a long-acting analogue insulin. Slightly longer onset and a fairly peakless profile of between 5 and 23 hours duration depending on the dose taken (bigger doses of most insulins tend to last longer). Levemir seems to be usually taken in two doses, roughly 12 hours apart. People who have differing overnight and daytime basal requirements can adust the two doses to match.
I've always been advised to keep doses the same when switching insulins, but to test more often to see how things are going. From your results it might be that you need an extra unit or two, and/or if you are injecting one dose in the evening it may be that the Levemir is not quite lasting 24 hours with a corresponding rise before the following injection.
If you have only recently changed, your body may still be 'settling in' to the new insulin. I changed my rapid-acting earlier this year and doses initially went down, before settling pretty much back up to the old levels.
If you do not usually adjust your own doses, and are not confident in doing so I'd suggest you get on to your care team as soon as possible and discuss it with them.