I entered a Marathon once .... I got a peanut stuck under my foreskin.
Now that's out of the way ... I did London a long time ago. I was running 10kms pretty quickly at the time (sub 35 mins) so naively thought the step up would be pretty simple and my only preparation was my normal 10km training (long runs of an hour at a steady, club pace; faster 5+kms and the occasional group fartlek) and one half marathon two weeks before the big day. In short, it wasn't. I pretty much discovered that my "natural" endurance threshold was around 1.5 hours and I went backwards after that. I ran it with a friend who was the opposite - he would get around 10km in 50 minutes, but could carry on at that pace for as long as he liked. He was a smoker, which annoyed me even more! We were both early twenties at the time.
I guess my point is that, in my experience, some are more naturally pre-disposed to endurance running than others. Those that aren't need to work more on their endurance. I wish I knew that when I did the marathon because frankly my experience that day (4hr50 having totally blown up at 17 miles) put me off doing it again!
If you're running 10kms now you're off to a strong start and your half marathon time is good enough to give you confidence you can step up. I don't think there's a shortcut to building marathon endurance, though and suspect that pounding the pavements is going to feature in your near future if you're going to enjoy the experience. The trick is to make it interesting, though. This could be following a training programme (Runners World website is very good) but that may not work for you. If you like running with headphones, try and audio book or podcast instead of music. If the course is going to involve hills, find some hills to run up and down.
For me, the most important part is time spent on your feet because nothing other than running 20 miles will reproduce the pain / experiece of legs that are 20 miles old.
Question for you: at the end of your half marathon, how were your legs?
And good luck