From the US side of things, you are working in the US and subject to US taxation. Because you're working for an overseas company that does not have a payroll presence in the US, you should be billing them for your work and not only paying self employment taxes (i.e. social security) but also making quarterly estimated tax payments.

I have heard that the UK recently changed some of their tax rules to extend taxation to some folks in situations like yours. Not sure of the details, but there is a tax treaty between the US and UK that is supposed to avoid double taxation. Chances are, if you're resident in the US, it's the US IRS that you should be paying your taxes to.

For those who work as "independent contractors" (like you are doing now), it is normally considered appropriate for the previous employer to raise the rate of pay by a reasonable amount in order to cover the additional taxes (employer's portion of taxes and social security) and the administrative costs of having to do one's own "payroll" and accounting work. You may want to find an accountant or enrolled agent to advise you here.
Cheers,
Bev