I've taken Lempsip (sachets, made into drinks) a few times while bfing and haven't noticed any side effects on ds2 or my supply.
I think I checked Kellymom, etc and it was the pseudoephrine that seemed to be more of a problem - presumably that's why Sudafed and Lemsip are said to be okay.
Kellymom says "Both pseudoephedrine and phenylephrine are generally considered to be safe for the breastfed baby, but pseudoephedrine may reduce milk supply.
Pseudoephedrine & milk supply: Thomas Hale Ph. D., a renowned breastfeeding pharmacologist (Breastfeeding Pharmacology), notes that "breastfeeding mothers with poor or marginal milk production should be exceedingly cautious in using pseudoephedrine" and that "it is apparent that mothers in late-stage lactation may be more sensitive to pseudoephedrine and have greater loss in milk production" (Medications and Mother's Milk, 2006 edition).
Many meds have been reformulated so they no longer contain pseudoephedrine -- they're using phenylephrine instead. Per Hale, "Because of pseudoephedrine's effect on milk production, many have concerns that phenylephrine may suppress milk production as well. There is no evidence that this occurs at all."
I took that to mean it was fine to take it occasionally. Sometimes paracetamol just doesn't do enough and you have to take something stronger.