That would depend on whether the U.K. citizen also has an EU passport and/or whether they have an existing right to live/work in the country they are commuting to/from. If either case applies , there are no restrictions so long as they have confined their commuting between the U.K. and whichever EU country or countries they have those rights in.
If the U.K. citizen has no EU passport in addition to their U.K. one, or a pre existing right to work in another EU country (or the relevant permits / paperwork) then the only EU country that they can continue to live/work/commute to or from without restriction is the Republic of Ireland.
Whichever way you look at it, it’s a horrible mess, and quite depressing - especially for those U.K. citizens that could see all the problems that might come our way if we left the EU….