Ranking Same Keywords in Different TLDs

I have a client that is ranking in two different English TLD's. How can I specifically try to increase the keyword rankings on one of the TLDs without creating a new site?

For example, my client is ranking for "web design services" in US and the UK. How can I increase the rankings for just the UK? Is this possible? Would building links from .uk websites help a lot?

Just curios. I know creating a TLD site would be the best route, but wanted to see if there is another way as well.

Cheers!

Building links on .uk domain should help however they are backlinks and will probably affect both rankings since google will index them.

on your google web master tools set your target country as UK. Also build links from .co.uk domains. This will help you to rank good in UK results. But beware, as you said your site already ranked good in US, you may loose ranking in US search when you point your site for UK only.

If im right building some pages with .uk .that should be right