This problem comes up often. A large Victorian style house with a relatively small Kitchen in a single storey brick extension at the back. These don't work well for modern family living, there are problems with condensation in the winter, and the links with the garden can be very poor. The existing conservatory would work well as a dining/play area if it wasn't either too hot or freezing cold for large parts of the year.
Our clients had seen another of our extensions nearby and wanted something similar, but more in keeping with the existing building. They needed a larger Kitchen/Dining/play area, a Utility area, with better links to the garden, and good daylighting.
A full width extension can make the existing rooms very dark. One solution is to use roof lights, which allow almost four times as much daylight into the building as vertical windows and greatly reduce the need for electrical lighting. We use our computer software to check that there aren't going to be problems with glare, and to calculate the effect on the temperatures and heating in the building.
These clients had experience of building and had the time available so we provided the drawings, the Schedule of Work, and advice on how to handle the building process, and they got on with it using a trusted builder friend. An advantage to them was not paying my fees though there are aspects of the detailing which I'd have liked to do differently. Here this process worked reasonably well, but sometimes due to the lack or experience and knowledge it can go very wrong.