Can a UK company hire me as a US based consultant to do work in USA and UK?

I have been approached by a UK public sector agency to get hired as an independent  contractor. I am a US citizen and will travel back and forth between UK and USA for this position. The role involves bringing a US based concept into UK and scaling it - so it it dependent upon using US based information that I have access to. Will this firm be able to hire me as an American, or will I need a visa to do this work?
Thanks for any advice you have.

Depends...  Will you just be traveling to the UK, as a US employee on a business trip (very short term, specific reason such as training or a conference)?  If not, you'll need a UK work visa.

If you will be performing work while you are in the UK, you need a visa.