A general purpose police dog, often a German Shepherd, is a ground scenting/trail dog. They are trained to pick up the strongest, freshest human scent and follow it, often with the intention to track an offender and 'detain' them.
If it was a general purpose police dog that was being used then it would have been of limited use in finding a body. Therefore the presence of the dog may have just been coincidental as the officer searched and for community reassurance.
Ideally, a specialist search dog with cadaver scenting skills would be required. If there are any such dogs available in UK police forces they will be few and far between based on the demand/cost curve. Such dogs are used by some search and rescue teams and are available from private companies.
What I do wonder is if a cadaver dog was used to try and identify if/where LB's body was stored in the Whitakers Arms/chicken sheds/coppice area prior to being moved to the cemetery.