This blog does not focus on trade. However, I get asked a lot of questions about how the agreements made by the government under its royal prerogative to make trade deals, are in practice scrutinised.
The UK trade policy observatory has written this useful blog on the subject here.
You can read there that the UK Parliament does not have a formal role. Although, in practice the government has taken to publishing trade objectives, and holding a limited parliamentary debate on them.
US – the USTR publishes its trade objectives (Feb 2019) – here.
UK – the UK publishes its trade objectives (April 2020) – here.
In practice, the UK-US FTA has not progressed. Mini-trade deals are also not agreed.