I'd start with the money first, if you haven't already.
How many days can you work over the year taking away holiday and a few for sickness? Then consider halving it (or maybe even less), they should be your billable days, the others are for biz dev & admin. Then take the amount you want to earn and divide.
Something like: 46 weeks x 5 days = 230 days, so 115 days to earn £40K is £347 a day or £50 an hour which is probably toward the high side for copywriting but isn't ridiculous...?
I find being specific about money really helps me to focus.
I (marketing freelancer) get most of my work from recommendation. So I use LinkedIn a lot to connect to people I meet as it helps to keep you top of mind if you share relevant content.
I produce a monthly enews and then share the blog articles across my social channels. I think having a social media presence is important too, as people check out mine to see what I am saying. It shows you are active. There are lots of websites of consultants/businesses that are dormant.
I also put myself forward for speaking and guest blog spots. I attend networking events too. I am always on the hustle!
What has helped me is being clear about my niche - do you have one? I re-branded last financial year and billed xx% more than the year before. I wonder how willing local companies will be to pay for professional copywriting? Agencies might be a better bet?
I think emailing potential clients is fine, but I'd try to be as tailored as you can. Look at their site, social channels - be relevant with your comments. Think about the problems you can solve - ie great affordable copy which will help them deliver to their clients etc.
I would also think about handwritten or hardcopy leaflets/notes. They stand out today...Marketing agency ppl might appreciate a creative approach. If your niche is healthcare you could send some plasters etc. Or if they win an industry award drop off a bottle of Prosecco with a note? You want to get their attention...
I would suggest the message is 'I am a copywriter, I'd love to help you by providing great copy when you next need freelance help'? I'd keep it simple?
Do you know any agency people you can ask about how they choose their freelance suppliers? I am sure it is recommendation or people they have met.
Have you checked if there are LinkedIn and Facebook Groups relevant to your niche, it is a good way to make contacts and potentially to pick up work.