In his first term in Parliament Geraint was appointed Chair of the Environment, Transport & Regions Departmental Committee and served on the Public Accounts Committee.
After 2001, Davies was appointed NSPCC Parliamentary Ambassador in 2003 (-2005) following his proposed Regulation of Childcare Providers Bill in April 2003, which meant child minders were no longer permitted to smack children and parents had the right to see records of complaints about prospective child minders in respect of child safety. These provisions were subsequently adopted by Government.
Geraint then proposed the Physical Punishment of Children (Prohibition) Bill in July 2003 which made striking children across the head or shaking them illegal. He sought to address children’s issues with a Healthy Children Manifesto (June 2004) to ban junk food advertising to children and regulate food labelling (adopted by Government 11/06) and a School Meals and Nutrition Bill in January 2005 that sought to include nutrition as part of inspections and to ban unhealthy vending (provisions adopted 3/05 & 10/05).
Geraint also sponsored the Regulation of Hormone Disrupting Chemicals Bill (May 2004) to impose precautionary bans on chemicals with evidence of them being dangerous. This bill was incorporated in the EU REACH directive 09/06 and supported by the World Wide Fund for Nature UK. He was also involved in a high profile campaign for the release of British detainees being held at Guantanamo Bay.
On his election for Swansea West in 2010, Geraint became the first newly elected MP to present a private bill - The Credit Card Regulation (child pornography) Bill July 2010 that received national media coverage and cross party support including an Early Day Motion signed by 203 MPs. The Bill penalises credit and debit card companies for facilitating the downloading of child abuse images and requires that pre-paid credit cards below £100 are only issued when the identity of those buying them is recorded in order trace their source if used for illegal downloading or underage purchases of weapons or alcohol.
In 2012, Geraint stepped up his campaign for electrifying the train route between Cardiff and Swansea by bringing together key Welsh stakeholders including major businesses in the area. This was eventually successful and the electrification is due to go ahead.
Geraint has campaigned against the closure of Remploy factories, which have employed disabled people since the Second World War. As a result of his efforts, the Fforestfach Remploy factory increased its orders and turnover. In March 2012, he introduced an Early Day Motion calling on the Government to devolve Remploy's Welsh assets to the Welsh Government.
Thanks to the work of Geraint and other local MPs together with Unite the Union, former Ford workers at the company's Jersey Marine factory won £29 million in compensation from Ford, which had underfunded the pension scheme when it transferred the site and workers to a separate company called Visteon.
Geraint Has put a Bill to Parliament proposing a moratorium on fracking. He has also asked for strict environmental controls on water and air pollution from fracking, effectively stopping an unregulated rush to scar and poison Wales. He has also proposed this to the Council of Europe, expressing concerns about environmental damage in the Swansea Bay area.
Geraint has put a Bill forward to Parliament to regulate psychotherapists and to ban gay-to-straight conversion therapies. Geraint believes the people using these methods have damaged many LGBT people for life, and Britain should lead the way in banning these people from operating as therapists. The Bill received cross-party support.
Geraint has expressed concerns regarding the Transatlantic Trade and Investment Partnership Agreement, voicing these issues to the Prime Minister in Parliament. Although supporting the streamlining of economic activity between Europe and the USA, Geraint raised concerns with certain clauses in TTIP, which is being negotiated in secret, which allows private companies to sue democratically elected governments if laws impact on their profits. The Prime minister, when responding to Geraint’s Bill, said he hoped it would allow MPs to scrutinise the agreement more openly.
In 2014, Geraint proposed a Bill to outlaw so called ‘revenge porn’ – where a partner would upload sexually explicit material of an ex-partner to a website after a break up. This received cross-party support and the Justice Secretary announced that this Bill would now be put into effect, successfully leading to a ban on this material.
Davies has also proposed a number of health related Bills, such as prohibiting the advertising of e-cigarettes and banning the sale of these new cigarettes to children. Geraint also proposed that foods be labelled more accurately, such as added sugar content being expressed in teaspoonfuls, with an annual target to be set by the Secretary of State for Health.