Complex sentence: Afterwards, he began an M.Phil at LSE, but left in 1970 and began working at the GCHQ, and in 1973 began working at the UK Foreign and Commonwealth Office.
Split into simpler sentences: Afterwards, he began an M.Phil at LSE, but left in 1970. After school he worked at the GCHQ, and in 1973 began working at the UK Foreign and Commonwealth Office.