The others are right, with all parts of the event if you start small and just keep cracking away things will click and the speed and distance will come with time. I always improve when I race because the mad competitive streak comes out - but I have a tendency to potter when I train on my own.
Trewbie, I like reading your posts. Is there a parkrun near you? It might be good to get a regular 5k in so you can measure your improvement from week to week. Ideally if there was one a few miles ride away you could combine bike and run training on Saturday mornings.