In most cases, installing a multi-fuel stove in the UK does not require planning permission. Permitted Development Rights (PDR) allow homeowners to make certain improvements to their property without seeking planning permission. Under PDR, you can install a multi-fuel stove, provided it meets specific criteria, such as not being installed on a listed building or within a designated conservation area. However, it is always recommended to consult with your local planning authority or a professional installer to ensure compliance with local regulations.