I need to get security clearance for a job and was wondering if the security vetting process would show I'm in a civil partnership, unless I declare it. The security check would be the basic check which I assume wouldn't involve investigating a persons marriage status. Am I right in thinking all they are interested in is checking whether I have a criminal background and my immigration status?

Background check only indicates criminal activities or not.

It just all depends on what level of check they do, and where they do it at Are they going to the local police station and doing a check, Or will they pay a online company for a background check.

Unless you ave registered your civil partner, there should be no record of it "officially"

But no, a basic search will be normally just criminal, sometimes criminal and credit.