I had a new tap fitting installed. None of the pipework was touched. Since then, every time I turn the tap on it starts banging.

Can I solve this myself or do I need a plumber?

When you say "tap" do you mean Garden Hose Valve or regular sink Faucet ?

If hose valve, than you bought one that has lose washer inside.

Same may be with regular sink faucet. But first, before you do anything: Open and Close your Angle Stops below the sink. They are may be source of the "banging" sound.

Please describe the "tap". Its function? If a faucet is it one handle or two knobs? The brand nameof the tap you installed? In short we need more detaiuls before we can give you a answer. Regards, Tom