Kestrel,
I will qualify my original Answer.
IMHO, the best way to improve is to ensure that you have plenty of 20 Mile runs under your belt. It sounds like you have some speed already. The issue the last time is that you started to struggle ( and therefore slowed down) around 10 Miles. This means enduarance was the problem.... eg you were unable to keep up your speed as you got later into the race.
The way to avoid this is to do lots of long runs. I do not think 2x18 mile runs and a 20 Mile run is enough if you wish to keep your pace towards the end. Or to put it another way if you did 5 x 20 mile runs then you will fair far better.
The issue is that you cannot just start your training plan from a lower base and pile in 5X20 milers in 12-16 weeks if you are not used to it. This is why I say get used to running long now before you getto your formal training plan. Get used to running say 15 miles every other weekend. Come race day you find it easy to run 15-20 miles as you will have done it so many times. With a good taper it will seem "easy" to run thsi distance.
This in itself will mean you will run a faster time than you did last time as you will not slow down so much.
The benefit of lots of "long Runs" is that it helps you be more efficient in your running. This also will help you in your shorter runs. Lots of folk improve their times in shorter races when they do marathon training for this reason.
I agree with One gear as to the 3 things that will help you improve. My view is that more long runs is the most important for marathon training. That said its also good to try and run some of your shorter runs faster. Things like intervals and tempo runs are good, however you do not want to tire yourself out too much so that you do not do your long training runs. Whilst its not everyones cup of tea a regular parkrun done twice a month may help you get faster over shorter distances and this would complement your regular longer runs.
To help back up some of my views heres some data of my own.
I did my first marathon in 4:09. I ran 500 Miles in the 16 weeks before the marathon. I did a 16,17,18,19+20 miles for my long runs in advance but I really slowed in the last 3-4 miles.
Then 7 Months later I ran 3:34. This time I ran 660 Miles in the 16 Miles before this marathon and did more long runs beween 20-23 Miles. This time I ran strong to the end with an even pace.
For both races I did not do a lot of faster shorter runs. I did semi regular parkruns. These helped. For my next marathon I am doing some faster intervals etc. However I would have "broke" had I tried to increase my mileage and do lots of faster runs.
So I think you will improve speed ( or rather not slow down and run faster as a result) if you increase mileage only. There is more than one way to skin a cat - but be careful not trying to do everything too soon or you may end up with Injury and get a virus etc...
Good Luck...
Edited: 18/08/2012 at 15:31