Yes, converting a shop or other commercial unit into a residential dwelling is a material change of use and requires planning permission, and the site's zoning must generally allow residential use for the application to succeed. The proposal will also need to meet residential design standards and Building Regulations even where no major structural work is involved.
Turning a retail unit or other commercial premises into a home is a clear material change of use between planning use classes and requires planning permission from the local authority. Local authorities assess these applications not just on the physical suitability of the building, but on whether residential use is appropriate for that location and consistent with the zoning objective in the county or city development plan, since some town centre and neighbourhood centre zonings specifically aim to protect ground-floor commercial or retail frontage.
Where the zoning does support residential use, or mixed-use development, the application will still need to address matters such as adequate natural light and ventilation, noise from adjoining commercial units, private amenity space, refuse storage, and parking, all of which shops are rarely designed to provide and which may require redesign of the internal layout or an extension to achieve compliance.
In town and village centres, some local authorities actively support 'living over the shop' or vacant premises conversion schemes to bring empty commercial buildings back into use, sometimes with grant support, so it's worth checking whether such incentives apply in addition to the standard planning process.