It has been possible for some time for home educated young people to access college places for free under a special arrangement providing the college agrees to it.
This is a special arrangement specifically set up for home educated young people whereby the parents remain primarily responsible for the child's welfare and general education, so the college does not have to offer a full time education or provide pastoral care. In some respects, it's a little like flexi schooling.
Funding is available through the post 16 funding formula. Not all colleges are aware of how this works and many don't yet offer this as an option. Even where they do offer courses, they may not offer the course you want. However, if this is something you may be interested in, it's worth looking into.
Colleges are a different environment to schools and some thought should be given to whether your child would suit such an environment at their current age. On the other hand colleges can be an excellent alternative to schools in certain circumstances and some home educated young people have made excellent use of them in moving on to higher education or vocational courses. The fact that they are free can also be very useful in gaining any necessary GCSE courses, where your local college offers them.
Even where a college does offer courses,
or is aware of and open to, such arrangements, many of the staff are
not aware. So, it's likely that if you attend an open day you will be
told that it's not possible. You should attempt to find out if there
is anyone designated as being in charge of such arrangements or speak
to either the principle or head of departments.
Be well versed on the arrangements, download and read the funding formula (of particular interest is LDM code 321 which is the code used by a college to access funding.)