Hey Tom - I'm in a very similar situation to you, as I also missed lots of school and didn't sit any GCSEs. I'm now 18 and am still doing a few GCSEs this year before going into sixth form. I don't know whether this would work for you but I did 4 GCSEs in one year and I'm doing 3 this year.
This is just an idea about what you could do:
English Language (instead of Literature) - I would have preferred literature as well, but it's very hard to find a place that teaches it. English Language is offered in sixth form/FE colleges usually as an evening class and the course involves quite a lot of literature (we did Hamlet, To Kill a Mockingbird and an anthology of poems!).
Maths - If you don't already have this, it's a very good idea to get it because jobs and courses often ask for applicants to have a grade C or equivalent in mathematics. You could probably do this at a local college, too.
History and Geography - I was lucky to have a tutor for history, but you can do both of these subjects through correspondence courses. The courses are quite good, but they are often expensive and you have to find an exam centre so you can sit the exams at the end of the year. I'd recommend NEC - National Extension College.
A Language - I'm doing Spanish through an NEC correspondence course. It's very helpful and comes with CDs, notes and books as well as a tutor you can email and send work to. Again, some sixth form colleges do language courses in the evenings - usually either French, Spanish or German.
As someone else suggested, an Access Course isn't a bad idea; however, I think it's A-level standard so maybe it would be a good idea to do GCSEs first in one year and then go on to do that.