(2-part post):
Long ferry journeys usually cost far more than air travel over the same route. Travelling in the summer months you'd have to get right up to northern tip of Scotland (which is expensive enough to start with, unless you're already close by) to pick up the Smyril Line ferry to Seydisfj�rdur (which is a 7 hour bus ride away from Reykjavik). At other times, you'd have to take a DFDS ferry from Newcastle to Bergen and then take the Smyril Line ferry from there. With 3 nights accommodation to pay for, it certainly wouldn't be cheap. From October to March, passengers aren't carried at all on the ferries, because the seas are so rough. (You might still experience some quite horrendous conditions at other times of the year, as well):
http://www.seat61.com/Iceland.htm
Germanwings (who're usually fairly cheap) fly to Kefvlavik International Airport (which serves Reykjavik) from both Dublin and Edinburgh. There are loads of cheap flights to Dublin (e.g. with Ryanair) from most parts of the UK, so that's one possible route.