There is no technical problem with .uk.com - the only "problem" might be in terms of perception, as it's neither nnnnnn.com or nnnnnnn.co.uk, which are the domains most people associate with UK businesses (leaving .net and .org aside).
I think that the whole TLD structure has been a dog's breakfast from day one, with the USA not being country-specific like everyone else (OK, they built the original system!), then everyone else using non-country-specific TLDs anyway - and the introduction of all sorts of additional TLDs has just made it messier.
Embrace the free-for-all and good luck to you!
SD