Yes you can, but unfortunately it isn’t as straight forward as this as you may need planning permission. The planning Portal page Class E(a) states that the building should be incidental. A garden office or studio used for leisure may well be viewed as incidental whereas as garden office, studio used for business 5 days a week may well need planning permission. Each local authority interprets the permitted development rules differently and in addition to this, the government doesn’t give a clear definition of what an ‘incidental’ building is. If you are considering running a business from your garden building then it is advised that you get in touch with your local planning authority (LPA) and attempt to get confirmation in writing either way.