There are a number of reputable websites that sell used phones including Decluttr, Backmarket, and Swappa.
What's the best second-hand phone to buy?
It depends on what phone you're looking for. You'll find most handsets available second-hand at a much cheaper price.
Is buying a used phone worth it?
If you're looking to upgrade your phone and save yourself money then buying a used or refurbished phone can help you get much more bang for your buck. Bear in mind that used phones are sold as seen, they've not had any repairs done to them, unlike refurbished phones.