Working in the US?

[Zapatero]

I am a British-born UK-based freelancer writer/editor and I am looking to move to the US as a full-time student next year. I would need to continue working for my main client to fund my studies (which they are happy for me to do), but I'm unsure about the tax and visa situation:

As I will be a full-time mature international student, studying under the constraints of a (F-1) visa, I'm not sure if I am even allowed to work. That said, if the work is done in my place of residence, for a UK-based organisation with payments being made into a UK bank account, what would it matter?

If I could work (or did so "stealthily"), what would be the tax implications? Would I be liable to pay taxes to the UK Government and how might this be affected by me being a full-time student in another country?

Thanks in advance.

- Z