This goes back much further than reported.

In the early 1970s, United ran a large network of services in Northumberland and Durham (before Tyne and Wear was thought of). In both areas service numbers were usually single- or double digits.
This led to one anomaly in Newcastle where the Durham service 56 ran to Bishop Auckland and the Northumberland 56 ran to Dudley.
Between 1970 and 1971 United decided to renumber the Northumberland services with 3 digits. This was to get rid of anomalies and also to avoid using letter suffixes. The 1971 timetable shows services in Ashington, Blyth and Cramlington coming down to the Tyne allocated 3xx. 3xx extended along the Tyne Valley to Hexham and Carlisle. 4xx was also used in the Ashington/Blyth area (the present-day 308 was, for a while 408) and 4xx extended further north into Northumberland. 5xx was used for the Edinburgh services from Newcastle via Berwick, Wooler or Carter Bar.
There was also a large number of services operated by private operators and most of these were numbered 8xx (hence the 808 which still runs with that number today).
Around the time when the Metro started running in 1980, the Tyne and Wear Passenger Transport Executive changed many route numbers. As correctly reported above, these included 5xx for South Tyneside, 6xx for areas west of Gateshead on the south side of the Tyne, and 7xx for services further into County Durham.

Re the point raised about Nexus returning to the 3-digit format for North Tyneside: they have been using this for a long time, for example the (soon to disappear) 359 and the 319 which until last year linked North Shields through the Tunnel to Jarrow. One last point, new service 317 isn’t new. That number was allocated to the Whitley Bay – North Shields Ferry service around 1980 (see above). In recent years the service was amalgamated with the North Shields – Wallsend (and beyond) service (at one time the 313), then renumbered 17 then renumbered again to the present day 11.