Getting to Iceland from UK

I'm getting married at the end of next April and for our honeymoon we're pretty much set on Iceland. We normally travel with budget airlines to continental Europe, and I haven't had much luck finding a budget airline who cover Iceland, so I have two questions. Firstly, is there a budget airline who cover Iceland who've I've just not found? And secondly, when would the best time be to book tickets in order to ensure we get them for the absolute cheapest price we can (i.e. would now be too early or is it the earlier the better with "normal" airlines)?
Thanks!

Iceland Express is a budget airline - which as usual does not mean that all their seats are cheaper than the cheapest seat on the other two airlines that fly GB_Iceland: Icelandair (semi-budget) and BA - occitionally the regulars are cheaper (in total price).

But Iceland Express follow the discounts airlines rules (no guarantee for anything - not everything included in the price you see)

BA this summer not have flight to KEF more.

i tried Icelandexpress on June but unfortunately, got totally 20 hours delay (11hrs in Gatwick and 9 hours in KEF....) i am not a lucky guy...

Thanks for the help guys! I'll check out Iceland Express (and hope we wouldn't be as unlucky as you mantse) and see if they're any cheaper than Icelandair or BA.