This is a tricky one! If you are buying the original badges and simply incorporating them into a necklace, I don't think there's any copyright infringement because, firstly, you are not copying
the image, but paying for it legitimately and using it as is, and you are not making a derivative work in the sense that the Copyright Designs and Patents Act refers to.
I think if
there is any problem it might lie with exploitation of a Trademark. Many cartoon characters are also registered as trademarks in order to safeguard their use on promotional or spinoff merchandise. A licence is normally required to produce trademarked items. As what you are proposing may
fall into this category, I suggest you consult a lawyer who specialises in Intellectual Property law which will include Trademarks. But before doing that you could go to the IP Ofiice website www.ipo.gov.uk
and search for your cartoon character on the trademark database to see if it has been registered (I think you need to look in Class 41). This quite tricky as you need to define the type of image in order to do the search. For example I just did a search on the Simpsons using 'simpsons' in the text string search and category 02 'humans' in the image class, and it returned several relevent trademarks. If your cartoon features an animal or some object obviously you will need to change that bit. If you do need to consult a lawyer, there are links on the IPO website to various professional bodies of lawyers specialising in IP law.
Sorry not to be more precise, but unfortunately this is an area of IP law where my knowledge is limited.