Apparently there is an organization called the CES (Catholic Education Services) that SHOULD BE DEFENDING Catholic homeschoolers in the UK but instead have sided with their government for not so friendly terms in establishing laws and/or regulations regarding homeschooling in the UK.
Read this to start with: CES broadly supports Government Homeschooling proposal
I am not completely well versed in the history or current state of homeschooling in the UK. However it seems like it is what the US was like with homeschooling in the late 70′s and 80′s. I think the homeschoolers in the UK would value much from hearing from those veteran homeschooling parents who fought for it to be legal in the US. I do not know how to find this group of people, so you will have to find me. If you are someone whom I should thank with all my heart for reaping the fruit of your struggle and sacrifice, please email me at firstname.lastname@example.org if you would like to assist homeschooling family in the UK in their struggle.