How soon until I get faster?

I've started back running and I'm on a 30 week training programme for the Dublin Marathon at the end of October. I'm a 5ft 10 male, weighing 16.5 stone so I'm about 4-5 stone overweight.

My pace at the moment is very slow. I think I've broken 40 minutes for a 5k twice, but only just dipped into the 39 minute range and even then, that was over a year ago. Now, 5k usually takes me about 42 minutes. I used the MacMillan running calculator and it says a marathon will take me 6hrs 51 minutes based on my 5k time! That is far far too long. If I run consistently for the next 7 months and drop some weight, how much faster am I likely to get? This is without doing any specific speed work.

You will naturally get a little quicker as you get gradually fitter.
How much quicker is impossible to tell, we're all different!
But I would suggest that you do start to include a little speed work - it doesn't have to be anything too dramatic! Just try a few short quicker spurts now and then in your normal runs and build from there. Just be careful not to push too much and damage anything!
If you can start to train yourself to run at a quicker pace, even if just for short distances, you'll soon find your natural pace picking up a bit without having to go bonkers with interval sessions.
Mind you - once you feel up to it - interval sessions are very good for you!

This very roughly predicts 8 secs speed increase for each lb lost, over a 5km distance.

http://www.runningforfitness.org/calc/diet/weighteffect?metres=5000&hr=0&min=40&sec=0&weight=225&weightunits=lbs&Submit=Calculate

As you drop weight and get fitter you will natrually get quicker. Remember to listen to your body, rest is as important as running.

Thanks.

Yeah I want to stay injury free so I'm going to be careful.  I'm following this plan

http://www.halhigdon.com/training/51143/Marathon-Novice-Supreme-Training-Program

Which seems nice and has a decent base training period build in which is what I need at the moment.

When you mention doing intervals, what would people suggest?  My distances at the moment are very short, between 1.5 and 3.5 miles.  So something like maybe running a bit faster for 100 metres every half mile or something?

Yes I think that would be a good start and once you get to about week 10 in that schedule it might be an idea to do one of the shorter runs in that week at a faster pace (after warming up gently for about a mile).
I also think variety is very good so it would be worth trying some hill reps and half mile intervals when you start to get into a bit of speed work. (But probably best to only do one session of speed work each week)
It's very easy to get into the habit of only running at one pace and staying at that pace even when you're improving!
Most of all - have fun and enjoy running!