For the colors of the graphical elements, I am quite open. It can be set of blues, but also yellow/red, up to purple or pink might be an option.
Our Ideas and Additional Information:
The domain name (businesscards.uk or BUSINESSCARDS.UK) is critical for the website and brand. Therefore it is important to include the TLD (.uk) in the logo.
The challenge is the combination of the url and a brandable style. The logo might be only the text, which is enhanced by some graphical element, or can be a symbol (logo) and the name, whereas the symbol could consist "bc" or better something which refers to business cards, printing and/or customization.