A 301 redirect is not going to help in your case: search engines treat a 301 redirect from A to B as in instruction to index the URL B instead of A. Thus, your
.co.uk domain will never show up in Google results, since it contains nothing but 301 redirects.
(I suppose it is possible that the existence of the
.co.uk domain may affect Google's geotargeting algorithms, at least if other sites mainly link to it rather than to the
.co domain — I don't really have any hard data or authoritative information on that.)
Instead, you and your friend should make the site itself appear under the
.co.uk domain. From your end, this may be as simple as configuring a DNS alias (a CNAME record) from
hissite.co. If your friend's site is on a dedicated server (or an IP-based virtual host), this will be enough; however, if it's on a name-based virtual host, the webserver will also have to be configured to recognize
hissite.co.uk as an alias for your friend's website.
You and/or your friend may want to contact your friend's hosting provider and ask them how to best set this up; they may be willing to help, or even to suggest an easier (or cheaper) way than what I've described above.
Once you've got the site working under both domains, I'd recommend setting the original
.co domain to return 301 redirects to the
.co.uk domain. That way, you won't have the same content appearing on two different domains, which could cause SEO issues (not to mention general user confusion).
If you can't or don't want to do that for some reason, you could also tell your friend to register his site on Google's Webmaster Tools and use the geotargeting settings there to target the site for users in the UK. Normally this is not possible for sites under a country-specific TLD, but fortunately for your friend, Google treats
.co as a generic top-level domain, and so allows changing the geotargeting settings for sites under it.
Another trick that might work would be to replace your 301 redirects with 302s and have your friend include a
rel=canonical meta tag on all his pages pointing to the corresponding URL on the
.co.uk domain. However, I really would rather recommend just trying to make the site appear under the correct domain in the first place.
.co.uk site to act as a transparent proxy for your friend's site, as LazyOne suggests in the comments, is also one solution, but not one I'd recommend either. From the user's viewpoint, it will look pretty much the same as a DNS alias, but it's more technically complex and thus typically slower and more prone to failure. Its one advantage over a DNS alias is that you can set up such proxying entirely from your end, even if your friend's site is hosted on a name-based virtual host.