On 24th May 2019, the House of Commons library published a useful 92-page Briefing Paper on the process of replacing EU treaties ( to which the UK is currently a party by virtue of its membership of the EU) with UK treaties.
These UK replacement treaties would take effect from Brexit, if there is a "no deal" scenario, or from the end of the transitional/ implementation period, if any Brexit deal incorporates provision for such a transitional or implementation period.
The Briefing Paper confirms that there are around 800 bilateral or multilateral agreements with third states or organisations to which the UK is currently a party by virtue of its EU membership. These include many trade agreements ( with estimates varying from around 70 to over 100). Many others are trade-related or concern such important matters as environmental protection or co-operation in science, research or security.
According to the Briefing Paper, there were 31 new treaties which had been signed up by the UK with third parties by 21st March 2019 and which had completed their UK parliamentary approval process, with another 12 due to be completed within a week and another 4 about to begin their UK parliamentary approval process. This is all part of the UK Government's so-called "Treaty Continuity Programme".
The Briefing Paper highlights concerns about perceived flaws and a lack of transparency in the current process for scrutinising and approving the replacement UK treaties but also notes the expressed wishes of the UK Government to be more open and accountable about future UK trade negotiations generally, particularly in the context of post-Brexit Free Trade Agreements. A White Paper issued by the UK Government Department of International Trade in February 2019 focused on the need to involve Parliament more in the scrutiny of future Free Trade Agreements.
With the renewed attention on Brexit following the European Parliament election on 23rd May 2019, there may well be a stronger push to try and finalise replacement UK treaties as soon as possible and to prepare for future trade negotiations post-Brexit.