I will counter with leave it in. I've recently started applying for jobs; I'll be in Scotland on the 27th. I applied for a position the other day and one of the first things mentioned was my Visa Status. I do agree it draws attention, but if your resume shows nothing but American companies, you really need that clarifcation up front.
I really do think it depends on your circumstances and what information your CV has as to whether you leave it in or out.
If you are not in the UK yet (i.e. you are listing a US address), or as you said, all your work experience is in the US, then I would clarify that you do in fact have a visa that allows you to work in the UK... otherwise your application may be overlooked simply because they think you will need visa sponsorship for the job.
On the other hand, if you are in the UK already, have a UK address and you have some UK work experience, you would probably be okay to leave it out.
I guess it also depends whether you put your nationality on your CV or not - if you put US/American citizen on it, then you would need to clarify that you have permission to work in the UK, otherwise you may not be considered for the job. If you don't put your nationality on then you may not need to bother clarifying it.
As long as you do have a visa that allows work you should not be treated any differently by employers than if you were a UK/EU citizen... so it's going to depend on whether or not you feel it's important to emphasise your immigration status to ensure your application is treated fairly by that company.