Wrapping paper
Some wrapping paper is recyclable whilst other types are not. Plain wrapping paper can be recycled in your green bin or a paper bank at a Household Recycling Centre, but you must check whether it is the right type of paper (i.e. not glittery or plastic backed). The easiest way to tell is to do the 'scrunch test'. Scrunch the wrapping paper up into a ball. When you release your hand, if the paper remains in a ball then it is recyclable in your green bin as it will be paper based. If, when you open your hand, the paper springs back then it's likely to also have plastic mixed in and will need to go into your black/grey bin.
Alternatively you could use reusable gift bags or scarf wrapping which can both be reused many times.