One option would be to move the exchange date to March or to closer to March say Mid Feb. It's not unusual to have some kind of delay between agreeing an offer and exchange date and then a further gap to the completion date. Buildings Insurance is the key thing I know of you need to start from the date of exchange. I'm guessing you will have surveys that will need to be completed or further checks you might want to do (perhaps you have already done these).
If you want to negotiate further you can always do this until the date of exchange. But ultimately if you are happy with the price you are paying and they are happy with the price they are selling it may be best not to upset this balance.
Exchanging contracts early has the advantage that you are sealing the deal (assuming you are happy with it). Exchanging contracts later means that there is a risk that the seller pulls out. Normally mortgage offers are valid for a certain period of time (months) so as long as you are within that time it shouldn't be a problem.
Just realised I was replying to a post a few pages back @hovis so not sure if this still relevant!