As an American, I would look at the website. If the site stated that they had experience working for both American and British, International clients and things like spelling would conform to American norms I would have no problems with a .co.uk suffix. I've done this when looking for forums on several subjects, if they indicate the are UK only I don't join, but if they are UK but accept Americans I might stick around.
I used to hire a Canadian web designer, she was quite capable of using American spelling and her grammar and punctuation were impeccable. She did have a .com but there were really only three extensions back then. Likewise, I hosted a site with a U.K. host. Best hosting service I ever had.
But that is me. I do think there is the risk of getting shunted off into the UK only serps on G with a co.uk.
Where do you anticipate most of this site's referrals coming from, search engines or social WOM, or adverts? .co.uk might only be a hitch for people coming blindly from SE's.
