Quickest way would be to hire a GC that can complete it quickly. Recognize that you're going to sacrifice some quality for speed. If you're transforming a structure into a house, assuming that it's already dried in, find a good finish out contractor in your area.
If you're not worried about having a set of plans, you can go directly with your GC who can perform a design build on it, usually a lot quicker than an architectural firm.

Have you considered any constructors yet? I would recommend to start from getting a free quote from Fittra Construction https://www.fittra.co.uk/ as the most professional team. You see. this company is specializing on such cases and can provide you with all information required. Plus, you will get a detailed quote and they would stay in budget and in schedule. They will definitely assist you. Best of luck