The videos from the LMS lectures and all of the GRASP videos are now available again from the links you gave (for download, not streaming). Many apologies for their long hiatus offline and many thanks for your enthusiasm and persistence!! Please do email me for broken links etc., and I will update the site with some more recent materials.
Edit June 2022: The links have moved, the GRASP videos (including the LMS lectures) are available for download here.
While we're at it (and to compensate for these lectures being such a pain to track down), here is a link (hopefully even a working one?!?) to videos of my entire Spring 2021 graduate course From Maxwell to Langlands (or some name to that effect) about the Langlands program and electric-magnetic duality. Notes for these lectures are available from Arun Debray and Jackson Van Dyke (and the dream is to eventually turn these into a book, but I wouldn't hold my breath).