In 2010, Mathias was elected to the
London Borough of Richmond upon Thames as councillor for Hampton Wick. She was re-elected in 2014, but stepped down as a councillor shortly after becoming MP. At the
2015 general election, Mathias was elected as the MP for
Twickenham, defeating the
Liberal Democrat cabinet minister,
Vince Cable. She was appointed a member of the
Science and Technology Select Committee in July 2015. Mathias was defeated by Cable, by then knighted, in the
snap 2017 general election by almost 10,000 votes, when Cable won the highest vote share for the Liberal Democrats in any constituency nationally at 52.8%. She was one of five Conservative candidates who were controversially given £5,000 by a business run by a former Conservative party treasurer,
Michael Spencer, to fund their campaigns against Liberal Democrat opponents who had supported the EU "Remain" campaign.
Views In
Parliament, Mathias voted the same way as other Conservative MPs on the vast majority of issues. However, she voted differently from her colleagues on occasion, most consistently for: allowing terminally ill people to be given assistance to end their life, requiring pub companies to offer pub landlords rent-only leases, and for unilaterally guaranteeing the rights of EU citizens living in the UK; Mathias opposed US President
Donald Trump's refugee policy. She was opposed to
Brexit prior to the
2016 referendum. Mathias opposed of the
expansion of Heathrow Airport, and voiced her objection in the House of Commons on several occasions. She reacted negatively to the UK government's decision to begin consultation for the construction of a third runway, declaring expansion "misguided and not in the nation's interest". ==Personal life==