Ideally yes. Look for evidence of qualifications in construction or site management. For example an NVQ, City & Guilds diploma, HNC or HND.
Many local builders were originally joiners or bricklayers. Then decided to set up as general builders. So providing you with one point of contact for all the tradespersons needed. Such as electricians, heating engineers, plasterers etc. Not all local builders will have formal qualifications. But that doesn’t mean they are not good builders. If in doubt ask them to provide you with a references to satisfied customers.
Other reliable builders are members of the Chartered Institute of Building, CIOB, or members of the Federation of Master Builders, FMB. The websites of both can guide your selection.
Part of the full service of duties of an architect includes builders identification, assessment and selection.