Node 13 added supports for the locale option in the toLocaleString method. Before that, it was ignored and would always use the US formatting. As opposed the the US, the United Kingdom does not use mm/dd/yyyy as a date format:

Most style guides follow the DMY convention by recommending d mmmm yyyy (sometimes written dd/mm/yyyy) format in articles (Wikipedia)

As such, Node 13's behavior is correct. You're asking for a UK formatted date & getting one.

When doing the reverse:

The new Date() constructor will not accept just any arbitrary string as a date: it relies on what Date.parse() will recognize, which is basically ISO 8601 (YYYY-MM-DDThh:mm:ss) and "take a wild guess as a fallback"—which is not locale-aware and also implementation dependent. As it is impossible to tell if 01/02/2000 is DMY or MDY, no attempt is made to support both D/M/Y and M/D/Y, just the latter. You cannot tell Date.parse explicitly that you're feeding it a GB localized date.

MDN has an apt warning:

Note: Parsing of date strings with the Date constructor (and Date.parse(), which works the same way) is strongly discouraged due to browser differences and inconsistencies.

(Feeding it 2000-02-01T01:02:03Z would be fine)

There is no Date.parseFromLocaleString in the standard library. Perhaps a function to do this will be added to the spec in the future under the Intl.DateTimeFormat namespace. Third party libraries do have functions to help you with this, such as Day.js.

I recommend to never use a locale string as input for new Date(). Instead use a format made for it
new Date(new Date().toJSON());

close as working as designed? @nodejs/i18n-api