It could theoretically have a small effect. But only if Google has no other data to base geo-targeting on. If you have a .co.uk tld and/or set geo-targeting in WebMaster tools, and/or get backlinks from uk sites, it won't have any effect
If your target is the uk and you host on a us server make sure the host can pump it over to the uk fast enough. Some sites I visit over in Europe and other parts of the world can be rather slow loading over here in the u.s. Could be a number of other things involved, but make sure they do have a decent connection or backbone to the u.k. We do have plenty of slow loading sites here in the u.s. that are hosted in the u.s. too, some of them are overload with too many accounts. Pick a good u.s. hoster that can really pump it, or find a u.k. one that has good connectivity regionally.