See regulations for LMS prizes here.
The LMS also awards prizes in conjunction with other organisations, including the Institute of Mathematics and its Applications (IMA):
David Crighton Medal (awarded jointly with the IMA)
Christopher Zeeman Medal awarded jointly with the IMA)
Hirst Prize and Lectureship (awarded jointly with the British Society for the History of Mathematics)
Louis Bachelier Prize (awarded jointly with the Natixis Foundation for Quantitative Research and the Société de Mathématiques Appliquées et Industrielles (SMAI))
Scholarships and other awards:
A selection of the many prizes awarded to mathematicians throughout the world can be found here.