So long as your freelancer is working through their own company it should be easy for them to invoice a client overseas. Agree beforehand (like, when you ink the contract) on the payment currency so no party gets surprised by fluctuations. Also agree who pays the transfer charges, if any.
Since I have a company bank account it's relatively easy for clients to send an international transfer for the amount. You'll need an IBAN number from them (see http://www.paymentsuk.org.uk/policy/payments-industry-standa...) and given this, your bank should be able to make it happen.
In my experience payments from the US often get small amounts creamed off the top for unspecified (& probably illegal) "fees" by the various banks the money passes through. Generally I either take the hit or tack the missing amount onto the client's next invoice.
Another option - if you're feeling lucky - is simply to use PayPal. However be ready for them to hit you with fees (last time I looked it seemed to be around 2.5%) and you always run the risk of them impounding the money. While more effort, IBAN transfers are probably better.
Sounds like the process is smooth when they are working through a company but, how about paying individual contractors?
Most find it efficient to run a small business of their own (an accountant will handle 99% of the paperwork) but others - for example those who don't expect to be a contractor for long - can join an "umbrella company" operated by an accountant. Then they invoice via the umbrella company and most of the money passes back to them. Generally this has a higher cost & less scope for reducing the tax burden, but has the benefit of avoiding the long-term commitment of running your own company.