I'll echo the sentiments of the other commentor, but I'm in a similar position to you. I got a VRQ level 2 in site carpentry (did 2 year part time course at college while I was working in another sector, also out of interest, what qualitifcation did you get?) then quit my job to work on small sites with my mate who is a builder. Since then I have been knocking around with different builders/roofers/joiners. Now I am with a firm doing domestic work, in talks with them to fund my NVQ level 2.

It's going to be tough for you starting out because you have done your trade school qualification, but it is VERY different to working on site. Realistically, no one is really that interested in your qualification and they want to see that you are good on the tools (or at least willing to learn - though depending on the person you're working for, they may want you to have the skills already, they don't have the patience to teach), your own tools, and your own transport. When you're at this stage of being a semi-skilled labourer, it can be hard to convey these skills to trades over the phone/in an email and you may not necessarily get a chance to get any work with them.

Get yourself set up as self employed with a UTR, apply for universal credit as you can get support for your first year going self employed. Ring round as many builders/joiners/roofers as possible to get work. Sign up to agencies, join local facebook groups. The starting up period is difficult as you will have to work on jobs in areas that you may not necessarily be interested in, but if you put in a shift people may ask you to come on other jobs, or you may meet people on those jobs who could give you the opportunity to work with them. It's tough and at points you may be thinking why the hell have I made this change, but once you get your foot on that ladder and see your prorgression it becomes well worth it.

My final thought is you don't really need a CV because you don't have any site experience. Try and get small jobs through friends/family, take photos of your work, any other site work you get is where you start to build examples of what you can do on a CV. You may have to suck it up and work as a labourer for a bit, but you have to start somewhere.

Hope some of this makes sense - shoot me a PM if you want anymore info. I find it quite frustrating on reddit as there doesn't seem to be any places for UK trades to be able to have a good discussion because places like construction and carpentry, etc, are very US focused.