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][1]

A similar scheme exclusively for mathematics is funded by the [LMS][2].


  [1]: http://www.epsrc.ac.uk/skills/students/dta/vacationbursaries/
  [2]: http://www.lms.ac.uk/grants/undergraduate-research-bursaries