Cufflinks can be worn in so many situations these days. 'Cufflinks no tie' is no longer punishable by a long and painful death. In fact it's increasingly common which has made cufflinks appropriate to wear in a greater number of situations both at work and socially.
So, cufflinks are fine to be worn without a tie, and even without a jacket. However because of the lie of a French cuff shirt it is impractical to wear them with a jumper.
There are three main types of cufflink design commonly worn in the UK; Chainlink, Swivel (or torpedo back) and One-piece