A bit of politics crept into this Rag Week procession in the early 60's.
The "Ban The Bomb" symbol was a regular sight in 60's youth culture, and accompanying this particular parade were additional messages pinned to the car making sure their point was getting across to the public. One says "YOU CAN'T VACCINATE CHILDREN AGAINST NUCLEAR TESTS". Another has "JOIN US ON THE ALDERMASTON MARCH".
The location looks like the bottom of King Street to me.