The FT has come out this morning with some more specific examples of what exactly Davis is concerned about:
//The EU is systematically warning UK companies of a regulatory chill after Brexit as it seeks to accelerate the private sector’s preparations for a no-deal UK exit, according to recent legal notices reviewed by the Financial Times.
Even as negotiators neared a breakthrough in Brexit divorce talks, EU regulators issued a flurry of “be prepared” memos to about 15 industries in November and December, ranging from drugmakers, seafarers and mineral water producers to hauliers and airlines that rely on UK operating licences.
The documents call on companies to be ready for the UK to become “a third country” on March 29 2019, with no automatic right to operate in the single market. They also warn that operating licences will automatically lapse after Brexit and that many groups may have to create EU entities for continuity of business.
...
Brussels urges some chemicals groups to apply for approvals for biocidal products, such as disinfectants, from within the remaining 27 EU states so that the process is not affected by Brexit. “Holders of product authorisations must be established within the union,” it notes. Drugmakers are urged to revise product information because any UK representatives mentioned will be “obsolete” after March 2019.
One notice is dedicated to the implications for mineral water sourced in the UK, which can no longer be automatically marketed in the EU because they are “extracted from the ground of a third country”.
Highlighting the breadth of legal issues covered, the commission uses a memo to outline the detailed implications for certificates for slaughtering of animals for fur — a practice outlawed in the UK since 2000.
Only one EU notice to trademark holders explicitly mentions that the EU is “trying to agree solutions for some of the issues that might arise”. But in that case the main problem is for the EU side: the memo notes that legal protections for products such as champagne and parmesan will lapse in the UK after Brexit.//
Among the memos that the FT cites (which I don't have time to read through myself) are the following:
https://ec.europa.eu/transport/sites/transport/files/legislation/2017-12-11-notice-to-stakeholders-air-transport.pdf
https://ec.europa.eu/transport/sites/transport/files/legislation/2017-12-11-notice-to-stakeholders-road-transport.pdf
https://ec.europa.eu/food/sites/food/files/safety/docs/labelling-nutrition_mineral-waters_notice_business_operators_comm-art50_brexit_20171012.pdf
https://ec.europa.eu/transport/sites/transport/files/legislation/2017-12-11-notice-to-stakeholders-seafarer-qualifications.pdf
https://ec.europa.eu/health/sites/health/files/files/documents/ec_ema_notice_communication_brexit.pdf