UK figures on SIDS and co-sleeping are utterly mucked up by including sleeping in a chair or on a sofa with your baby along with sleeping in a bed with your baby. So unless you are very aware of the data limitations, they give an unecessarily dangerous view of co-sleeping.
Falling asleep on a chair / sofa with your baby is the most dangerous option in terms of SIDS or overlaying.
If in bed with you, your baby should be on a firm surface (so no to waterbeds should that be a possibility!), and not in danger of overheating. So not under your duvet, but in a grobag or own blanket. And not on a pillow, or with his head on your pillow. And on his back, just as he would be in a cot or basket.
Do not co-sleep if you or your partner have been drinking / smoking (even outside the house) / have taken drugs.
Most mothers curl around their baby, and there is some evidence that the breathing rates and body temperatures of mother and baby regulate one another when co-sleeping.
Countries with a norm of co-sleeping (Japan for eg) have far lower SIDS rates than the UK.
But, the official advice is baby in the same room as you for the first 6 months (so room sharing, not co-sleeping). I assume this is down to lack of good data on co-sleeping, and a risk minimisation attitude - there is nothing wrong or dangerous about room sharing, but some health professionals believe the jury is still out on co-sleeping.