Right, I'm just back from the osteopath, and feeling a lot more positive.
It's Achilles tendonitis. Apparently this is caused by micro-tears in the tendon, and is a repetitive strain type injury that can develop over time, and can emerge randomly like mine did, and not suddenly during running or turning ones heel over. The tendon runs from the bottom of the calf muscle and fans around the heel, so you can feel pain either side of the heel as well as down the back. He said the swelling wasn't a fluidy swelling, more a thickening of the tendon, so I probably caught it quite early.
He gave me a soft tissue massage around the injury, and acupuncture (my first time), and I'm going back on Monday to review the situation. No running for the time being, but he said when it was 90% healed, I'd be able to run cautiously.
I have to say, just from today's treatment it feels much better!
He said the advice he gives to runners who get an injury like this isn't to reduce the amount of running they do, but to mix it up - short sprints, intervals, perhaps cross-country.
Budge up on that couch, there!