Drama GCSE with all exam boards involves controlled assessment and so is difficult to arrange for private candidates; often home-educated students take alternative qualification such as dedicated drama exams.
Some home educators have arranged to take Drama GCSE in groups with a tutor - [The Otherwise Club] in North London for example. It is worth asking on your local Home Education email group and on the HE Exams Yahoogroup, and any other groups you are on eg Facebook pages, to see if a group might be available to you.
The only Drama IGCSE available in the UK is offered by CIE and the specification states that it is not available to private candidates.
There are alternative drama qualifications at GCSE level which you could do through a private drama class - similar to taking music grades. For example, Trinity College, LAMDA and New Era Academy are well-known drama exam boards which are accredited by OFQUAL and the awards have been given official status as equivalent to GCSE or A-level standard, etc. Briefly, a Level 1 qualification is equivalent to a GCSE grades D-G, Level 2 is equivalent to GCSE grades A*-C, and Level 3 is A-level standard. There's more detail about all these levels and equivalences from the DfE Qualifications Explained page.
For instance, the LAMDA and New Era Academy exams grades 4 and 5 are both accredited as Level 2 (GCSE equivalent) by OFQUAL. See
Trinity College, London offers the following awards which are officially recognised as Level 2:-
"Grades 4 - 5: Speech & Drama; Drama (Acting, Shakespeare, World Dramatists, Musical Theatre,
Performance Arts); Speech (Performing text); Communication Skills
Award in the Arts (Silver)" - download file via and overview of Trinity exams here: http://www.trinitycollege.co.uk/site/?id=139 Trinity Guildhall downloads
You could also do the Trinity Arts Award specialising in Drama - see Art for more information.
Drama exams at Level 3 (A-level standard) earn UCAS points for university entry - see http://www.ucas.com/documents/tariff/speechanddramajune2011.pdf
One benefit of taking a drama qualification through these boards is that you can specialise in different areas, and hopefully have more choice than you would at school - eg Musical Theatre, Shakespeare etc.. One parent comments: "I did New Era Academy exams as a teenager and found it much more interesting than the GCSE drama that I did at the same time. I liked the transparency of the system, and the fact that I was marked on my own work alone; in GCSE, if you have to put on a group performance then the overall standard of the group will be dependent on all its members, not just your child."
There are, of course, many drama groups which home-educated students can join in order to gain experience of working in group performances, and many home-ed students greatly enjoy these. As well as the wide variety of drama groups aimed at teenagers, some adult amateur dramatics groups may accept younger members.