I am assuming that (a) you are resident in the UK and (b) you are not domiciled here.
Yes. The income is taxed in the UK, but you get a tax break for any US taxes paid on them. This process is called remittance. You can learn about taxation here:
http://www.hmrc.gov.uk/pdfs/ir20.htm and specifically about this topic here:
http://www.hmrc.gov.uk/manuals/immanual/im1560.htm (and hit the "next page" button to cycle through the items).
While you are not a higher rate taxpayer, it may be worth your while hiring a UK specialist accountant to sort this type of thing out. Meanwhile, you should arrange to sort out your finances such that you are no longer exposed to remittance tax. Again, a UK tax specialist can provide this guidance for you.
I recommend James Reeves at james@jreeves.co.uk. He is reasonably priced, though he won't be able to help on the US side, just the UK (that makes him somewhat cheaper than a dual qualified person). Alternatively, you can shop for a dual qualified person or company, which will be somewhat more expensive - but at least it's all in one place.