Do you need a qualification to start a business as a handy man?

Generally no. Handyman is a general term for someone who offers their labour for a set, or agreed fee. However there are some site safety qualifications that would be beneficial to him for working on building sites, and some short courses on different trades which will make his services more desirable to customers. Check your national industry board I.e. Scottish industry board where you may find the shirt courses available. Also the government offers help and courses for starting new businesses. However they no longer provide funds.