I was mearly offering an alternative view, hence the words 'could' and 'may'.
Adzes, hammers, and big bloody axes are all possibilities
As for woodland coverage, pollen analysis shows a marked decline in the woodlands and evidence of intensive use of the landscape in the Late neolithic (earlier in some parts).
As this axe has been deemed to be Bronze Age then I would suggest that the landscape was being farmed even more intensively than during the Neolithic.