Structural engineer or architect?

From experience I would suggest you ask around in the local area and find a firm of builders that are experienced in working on your sort of property. Find out where they have carried out extensions or renovation work on old properties and don't be afraid to ask what the homeowners think of their work. This way you have a better chance of finding craftsmen that know how to work properly with the materials and techniques required. For example, avoid a builder who would use modern portland cement mortars on old stonework.

When you have found the right builder - based on your assessment of work you've seen - then you can ask them for a recommendation on producing a set of drawings. They may use a firm of surveyors to produce drawings and know a firm of engineers to do any structural calculations or they may have professionally qualified surveyors and engineers within their own firm.

Architects are very good at creative design but you already know what style your cottage extension has to follow. Get someone who can produce drawings that are practical and easy for the builders doing the work to follow - which is not always a strong point of architects.