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 in conjuction with the IMA)
Christopher Zeeman Medal awarded in conjuction with the IMA)
Louis Bachelier Prize (awarded in conjunction with the Natixis Foundation for Quantitative Research and the Société de Mathématiques Appliquées et Industrielles (SMAI))
Hirst Prize and Lectureship (awarded in conjunction with the British Society for the History of Mathematics).
Scholarships and other awards:
A selection of the many prizes awarded to mathematicians throughout the world can be found here.