The Labour MP backed several proposed amendments to the Trade Bill, but they were defeated in the House of Commons on Monday, July 20.
The health and social care aspect was defeated by 337 to 248 votes, with the majority Conservative government voting against the amendment.
Those voting in favour of the amendment were made up of all the other political parties, including those in Scotland, Wales and Northern Ireland.
In terms of health and the NHS these were "that no provision of that international trade agreement in any way undermines or restricts the ability of an appropriate authority" -
(a) to provide a comprehensive publicly funded health service free at the point of delivery,
(b) to protect the employment rights or terms and conditions of employment for public sector employees and those working in publicly funded health or care sectors,
(c) to regulate and maintain the quality and safety of health or care services,
(d) to regulate and control the pricing and reimbursement systems for the purchase of medicines or medical devices, or
(e) to regulate and maintain the level of protection afforded in relation to patient data, public health data and publicly provided social care data relating to UK citizens.
Other amendments to the Trade Bill included "agricultural goods imported under a free trade agreement may be imported into the UK only if the standards to which those goods were produced were as high as, or higher than, standards which at the time of import applied under UK law", relating to animal health and welfare, protection of the environment, food safety, hygiene and traceability, and plant health.
This amendment was also defeated by the majority government.
Government ministers say that the amendments were not needed - as they have maintained that no element of the NHS will be up for grabs in a future trade deal, and standards will not be lowered.
Ms Smith said: "I believe in a trade policy that is transparent and subject to full and meaningful parliamentary scrutiny, and so would have welcomed a Trade Bill that – in particular – provides for proper Parliamentary oversight of the specific trade deals at issue in the Bill, and for the negotiation, implementation or ratification of any future trade deals.
"With the government actively engaged in negotiations over those future trade deals with the US, Japan and other major economies, I would also have welcomed a Bill that would guarantee in law that these future agreements will not:
Undermine the UK’s current food and farming standards by allowing the import of agricultural products which fall below those standards;
Threaten the future of our NHS by forcing it open to competition from private service-providers in other countries; and
Row back on the protections for human rights, workers’ rights and the environment that have become mandatory in trade deals struck on the UK’s behalf by the EU.
"This Bill fails all of the above tests, and by failing to address the ‘scrutiny deficit’ that will arise once the European Parliament’s Committee on International Trade and the House of Commons European Scrutiny Committee become defunct, it leaves us with no means of correcting the failings of future trade deals entered into by the government.
"I therefore voted in favour of New Clause 4 which would have would have ensured proper parliamentary scrutiny of trade deals, both prior to and during treaty negotiation. Sadly, however the Government opposed this amendment and it was defeated by 326 votes to 263. I also voted against the Trade Bill at Third Reading but was again in a minority.
"I will continue to campaign for a transparent trade policy which protects our public services, food and environmental standards and workers’ rights.”