Peter, it sounds exactly like plantar fasciitis, which is a sprain or inflammation of the plantar fascia, the tough membrane that lines the sole of your foot.
It's often associated with tight achilles tendons, so the first approach is to start, or increase, your calf and hamstring stretches. That may be sufficient, since it sounds as if you're quite mildly affected.
Check your shoes and make sure your heel doesn't slip when you're running. That can cause a sort of repetitive strain on the heel part of your plantar fascia.
If that doesn't work, a biomechanical assessment with a view to seeing whether you need orthotics to redistribute the stresses going through your foot would be worthwhile. If the pain becomes severe or prolonged enough to interfere with normal walking, anti-inflammatory medication such as Ibuprofen 600mg up to 3 times a day would be worthwhile.
As a last resort, a steroid injection into the affected area may help (most GP practices have someone who can do this procedure) but it's a painful injection (and hurts for a couple of days afterwards too), it doesn't always work, and there's a risk that the steroid will weaken the plantar fascia and cause it to tear.
The outlook is very good - given time, plantar fasciitis tends to settle down by itself. But you're a runner, you're bound to be more impatient than that!
The most important thing - provided your symptoms aren't getting worse, it's fine to continue to run, although you may benefit from a change to non-weightbearing cross-training for some of your sessions.
Cheers, V-rap.
