The second link above included a summary of UK knife laws. Reading over that section briefly, it would appear that if you are engaged in an appropriate activity with the machete (or whatever), you would be just fine. it's when you walk into a bank or jewelry store with the machete that you get into trouble.

Any sentient LEO in any jurisdiction should alert when someone is toting something out of character with the surroundings or the ongoing activity...That's just good police work.