Complex sentence: After winning a scholarship, he studied PPE at Lady Margaret Hall, Oxford, where he was elected as President of the Students' Union from 1985-86 on the Liberal/SDP Alliance ticket.
Split into simpler sentences: After winning a scholarship, he studied Philosophy, Politics, and Economics at Lady Margaret Hall, Oxford. While there, he was elected as President of the Oxford University Student Union for the year 1985-86 on the Liberal/SDP Alliance ticket.