Copyright applies automatically to (among other things) written works, drawings, photographs, software and recordings. i.e. if you create any of those works, you automatically hold the copyright (unless you're working on behalf of someone else, who might then be the copyright holder). There's is no need to register that copyright (and, indeed, no formal process available for doing so).
However copyright does not apply to 'inventions', or to methods and processes for making things work. Anyway wishing to acquire protection for such things has to obtain a patent. (Unlike copyright protection, patent protection is not automatic).
Your question seems to refer to a situation where, unless the original designer had applied for a patent, the second company is free to produce a similar product without the permission of (or payment to) that designer.
For more detailed information, see here:
http://www.ipo.gov.uk/
Chris