A short briefing note on visiting, working and living in the EU post-Brexit has just been published by the House of Commons Library.
A section on future negotiations noted that “the government says that the EU’s decision to treat British citizens in line with Schengen Borders Code provisions for Third Country Nationals is regrettable. But it has confirmed that it is not seeking to achieve enhanced short-term visit visa-free arrangements, whether through bilateral agreements with individual Member States, or further discussions with the EU”.
https://researchbriefings.files.parliament.uk/documents/CBP-9157/CBP-9157.pdf