In the UK there is the EPSRC Vacation Bursary Scheme for undergraduates, which provides funding for students to undertake an individual research project under the supervision of a suitable advisor during the summer. I participated as an undergrad myself and found it to be a really good experience. As I understand it, the universities participating in the scheme deal with the organization, but there is some information available at the EPSRC website
A similar scheme exclusively for mathematics is funded by the LMS.
