I'm setting this out as merely the first answer, but I'd be interested in the rest of the story, from a US or other international perspective...
I did some very quick research which gave me this official link to the UK's phone authority, Ofcom, listing the numbers which can be used for TV drama etc to give 'real looking' numbers.
Telephone numbers for use in TV and radio drama programmes
Ofcom continues to receive requests for geographic numbers to be used
for TV and radio drama programmes.
Ofcom has therefore set out below a range of geographic telephone
numbers that are recommended for TV and radio drama purposes (1000
numbers within each geographic area code).
For example, for a London number, you can use the real area code, 020, then any number between 7946 0000 & 7946 0999 [so if you were very picky you'd notice you can only have a Central London number, not an Outer London one] but it does overall mean you can use very realistic numbers without accidentally giving out an actual real one.
I'm surprised the US doesn't appear to have a similar arrangement.