According to this piece, written by a staffer at the House of Commons Library, the Immigration Bill currently passing through the House of Commons will repeal the existing EU legislation on a date to be decided by regulation (i.e. when the Home Secretary decides to do so).
It also says that the new immigration arrangements will be decided and implemented by regulation under the Immigration Act 1971 - i.e. according to the whim of the Home Secretary.
Whilst government white papers do talk about implementation and transition periods from 29th March until 2020 or January 2021, there is very little detail on how the new immigration rules will work as related to EU visitors, except for a short section that suggests that EU nationals will be treated as non-visa nationals (like US nationals at present) and will not need a visa to visit the UK.
In short, the new regulations will be announced by the Home Secretary in due course, and EU citizens should expect to be able to visit the UK visa-free.
There are caveats, however.
- It's not at all clear what will happen in the period from 29th March
to the end of any implementation period.
- Since immigration policy is
implemented by regulation it can change at the whim of the government
at any time.
- Spain is making trouble over Gibraltar that could result
in UK citizens needing a visa to visit the EU. In this case it's
likely that EU visitors to Britain will also need visas.