Quotes from the Beeb, taken out of order, but vertabim from the same article;

The body was found lying on the ground, around five miles from Dr Kelly's home, a police spokeswoman said.

Well, that makes a 78.5 square mile search area.

He left his home in Southmoor, Abingdon, Oxfordshire, at about 1500 BST on Thursday and his family reported him missing at 2345 BST the same day.

The body was found at 0920 BST by a member of the police team searching for Dr Kelly in a wooded area at Harrowdown Hill, near Faringdon, Oxfordshire.

Note that is only 9 hours and 35 minutes after the family notified them he was missing, which would give a search rate of 8.25 square miles/hour, assuming that they searched an ever-increasing spiral from his home.

Police say Dr Kelly is an avid walker and has good local knowledge of the many footpaths surrounding his home.

That suggests that he didn't merely frequent one area. How did they find him so quickly?

I suppose that he could have told his wife where he was going. Or maybe he drove there, and the car was found early on.
He was reported missing only 8 hours and 45 minutes after leaving for his walk. Assuming a 3 hour walk, that's under 6 hours of 'missing' time. Has anybody ever tried to file a missing person report before? I was under the impression that the police generally don't want to know within the first 24 hours where adults are concerned. I suppose that the attention he has been getting could make them escalate their concerns.

My point is that not only is the timing of his death extremely suspicious, but so is the speed at which he was found. Was there a tip off? Or was it bloody good police work?

I suppose one thing that I've overlooked is that he was found by a member of the public out walking a dog. But the media usually reports that, which they haven't (yet).