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
This is a classic chainlink cufflink The more traditional fitting suitable for formal occasions. They show well from both sides of the cuff
This pair has swivel backs Slightly more contemporary. Easy to put on so ideal for everyday wear as well as more formal occasions
and this pair is a one-piece design Modern and easy to put on. Not quite as flexible as the other two fittings but they look sharp...