"Rock Bottom", which she wrote with Mike Moran originally for Blue Mink, was chosen as the UK entry in the Eurovision Song Contest 1977 and released on Polydor. The duo also wrote and performed the B-side, the amusing "You Shouldn't Say That". De Paul made history by being the first female to perform her own composition at the Eurovision Song Contest. As she later explained, as well as being an honour, taking part in Eurovision was a way to circumvent the legal wrangles that were preventing her from signing to a new record label. Although it was the favourite to win, it came second in the Eurovision Song Contest and went on to become a Top 20 hit in many European countries including France, Germany, Austria and Switzerland, where it reached the top of their singles chart. It was the 15th best selling single of 1977 in Switzerland and the 32nd best selling single in Germany. The Eurovision experience resulted in a formal offer to stand as a liberal parliamentary candidate by chief party whip John Pardoe. "It started when I shot my mouth off over the strike of BBC cameramen that threatened to black out the song contest in England", she recalled. Pardoe, deputy leader of the Liberal Party (UK), invited her to tea at the House of Commons and suggested that she run for a seat in Parliament. That year she also joined the Council of the Songwriters Guild of Great Britain, the only woman on the council at that time.