Working as a Student and Freelance

So I currently hold a student tier 4 visa which of course means I can work 20 hours a week during term days and non term days 30 hours. If I happen to be offered a full time job than my visa has to change to a Teir 2 visa.

This question is as a student, is it possible to be self employed, not working for clients in the UK and not offering services to those in the UK, but working for home country instead?

The visa restrictions do not highlight this rule beyond no self employment which should be the end of it, but further research suggests that foreign citizens,residing in the US via a spouse with a work visa, without a work visa are able to do online work for their home counties, but not without being "Greatly frowned upon by the government" and other cases of freelance workers from the UK who happen to be in the US.

Further trying to find the exact point where it say no self employment has evaded me due to the official government guide does not elaborate on it.

Anyone have experience with this complicated kind of situation? The easy answer of course is just get hired part time, but beyond that it would be lovely to know the restrictions.

Pages 65 and 66 address the restrictions on self employment.

https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/477366/T4_Migrant_Guidance_Nov_V1_0.pdf

I'm sure if the rules as they apply to you say no self employment, then it means no self employment, irrespective of who/where your clients are.

UK immigration rules have nothing to do with US immigration rules. Stick to the .gov.uk site.

Unfortunately it's a no go.  As you are in the UK, all earnings regardless of where the work originated are subject to taxes through HMRC.  Therefore your US hours are restricted to the hours granted from your visa (20 hours per week during term time).