Complex sentence: She was elected to the UKIP NEC in 2004 and became Chairman of the NEC and National Chairman in that year, during which she wrote "Bye, Bye English Legal System", which appeared on the UKIP website.
Split into simpler sentences: She was elected to the UKIP NEC in 2004 and became Chairman of the NEC and National Chairman in that year. During her time as Chairman she wrote "Bye, Bye English Legal System", which appeared on the UKIP website.