I have been informed by some that if you host your UK domain within the USA, it can alter search engine results… Is this true? If no information is entered in Google Webmaster Tools, Google will continue to make geographic associations largely based on the top-level domain (e.g. .co.uk or .ca) and the IP address of the web server from which the context was served.
What about if you have a .co.uk domain and a USA IP address? Will I get better rankings if it is all UK based?

Yes, you will get better ranking in UK searches if the hosting is in the UK. Of course you have to weigh up the extra cost of hosting in the UK to determine whether or not you think it would be worth it.