I disagree with some of the advice you have received so far. I strongly recommend that you do not bring up that you outsource the design work, unless specifically asked for it. In that case, I would just answer that you have a good relationship with a design company that you work with to create a design that fit your clients requirements.
If we look at this from the customers side, they want to know they only have to deal with one entity (you) for the entire project. They do not want to deal with multiple sub contractors, trying to get their website pieced together. This means, that you take on the project, and it is your responsibility that any of the sub contractors you use deliver their part. If any of them does not deliver, it is your responsibility and you should own up to it and not blame the sub contractor (even if it is their fault). I.e. Your next step is apologize to the client, and then take the required steps to solve the situation.
It is also usually never a good idea to give away anything for free (other than the advice quoted below) as surprisingly enough a client that get something for free, expects the world (i.e. better product, better service etc.). Instead tell your potential client that you are running a new customer discount, and can do their website with a 50% (i.e. X percentage) discount. If they ask you why you offer this high discount, just explain that you are building up a new customer base.
Finally, make certain you sign a contract with the clients, and the contract should also state deliverable, both on your side and theirs. I.e. what they should pay and when, when will you deliver the initial design draft, when do they need to deliver their content text by (assuming you dont write it for them) etc.
This is very good advice for a good/efficient way to build your initial portfolio. In addition, if you cater for local customers, there is a high chance they are familiar with the organization etc. you have created a website for. Which means that you can already have a tiny relationship with them, assuming they like the work you did for the organization.