The images of Barbie or Disney characters will be covered by copyright, but more importantly for your purposes they will also be protected as registered trade marks.
Obtaining a licence to use these characters is relatively straightforward as the major corporations like Disney and Mattel have departments specially set up to deal with licensing. You should contact them to discuss what you need and they will tailor a licence to your needs.
Just to give you a flavour, here's what Disney say about licensing on their website:
The Walt Disney Company has a large portfolio of intellectual property that the company manages through relationships with a range of licensees, vendors and retailers. Products bearing Disney characters, stories, songs and brand names include a wide range of categories such as apparel, footwear, toys, stationery, published materials, food, CDs and DVDs, home furnishings and consumer electronics, among others. Disney has granted rights to more than 8,000 businesses to use our intellectual property in the manufacture of such products. Some of these licensees are large, even global, companies and retailers, while many others are medium-sized and small companies located around the world.
The majority of Disney-branded products are manufactured by licensees, managed by Disney Consumer Products (DCP). Studio Entertainment, Parks and Resorts, Media Networks and Disney Internet Media Group also source Disney merchandise for retail sale or for promotional purposes through licensee and vendor relationships.
We use the term "licensee" when we refer to the companies to whom we license the rights to manufacture Disney merchandise for distribution or sale to others and "vendor" when we refer to the companies we engage to manufacture Disney merchandise for us. Our agreements with both licensees and vendors include specific obligations which licensees and vendors must secure from each factory and supplier they engage in producing Disney merchandise.
Example of a Licensee Relationship: Company X seeks to create a shirt with an image of Mickey Mouse. This company reaches out to Disney to negotiate and conclude a license agreement for the right to reproduce Mickey's image on shirts in exchange for certain licensing fees and royalties. Company X then produces the shirt through its own supply chain and sells it to consumers (or retailers).
Example of a Vendor Relationship: Disney seeks to create a shirt with a Mickey Mouse image. Disney reaches out to Company Y to negotiate and conclude a vendor agreement for the supply of shirts with Mickey Mouse's image. Company Y then produces the shirt through its own supply chain, and sells it to Disney for the agreed price.
You can contact Disney here
Mattel here: firstname.lastname@example.org
If you require to use any other characters not owned by these two corporations, try Google in the first instance, but if that does not give you the information you need, try going via the IPO
website to their database of registered trade marks and type in the name of the character. This should give you both the organisation which owns the mark, and also their trade mark agents in the UK.