In 1958 the North Eastern Region began running a promotion for a day rover ticket called a "Day-Line Ticket" — for the first two years they were known as "Day-Line Diesel Tickets".
There were two versions, a Northern Section and Southern Section, each covering different areas. The only overlap between the two was the section from Whitby Town to Grosmont. The maps also defined the traction on the routes: regular diesel; electric; partial diesel; or steam.
These are the maps from the June 1958 leaflets:
Purchase of the ticket in 1958 and 1959 included a 'souvenir medallion'. I've found two different versions of these:
Another in better condition can be found on flickr.
Introduced from 12th May 1958 there were three different issues of the leaflets that year. These, and all those in the following years, measured 5" x 8".
The ticket price was 15 shillings or 7/6 for children which remained the same until 1961.
The following is the second version which covered the summer timetable period from 9th June till 14th September. They contain a number of abreviated timetables and sample intineraries. Each issue noted the number of diesel coaches in use on the Region — the May issue had "over 380", this one had "over 390".
On the right is a section of the 15th September 1958 York - Harrogate timetable noting the extension.
The third 1958 issue for the winter months (till 31st December) omitted the timetables. There were now "over 520" diesel coaches in use.
The 1959 season began on 23rd March (the week leading to Easter Sunday on the 29th), no end date was given. There were now "over 600" diesel coaches in use.
While the ticket price remained the same as 1958, this year there was a "High Season Charge" from July 6th to August 30th making the price 16/6 or 8/3.
For the 1960 season "Diesel" was dropped from the name as was the free medallion. The season began on 11th April (again the week leading to Easter, Easter Sunday being the 17th). There were now "over 700" diesel coaches in use. Cover only shown for the Southern section.
For 1961 the date moved to the back page of the pamphlet and began on March 27, again the week leading to Easter which was on the 2nd April.
The number of diesel coaches in use was no longer shown, and the price increased for the first time to 17 shillings or 8/9 for children. Cover only shown for the Southern section.
The 1962 season began on Monday 2nd April - a break from the traditional week leading to Easter Sunday which was not until the 22nd. Only the cover of the Southern Section is shown here.
For the first time the design was repeated from a previous year, but different colours were used. Ticket prices were now 20 shillings and 10 shillings, and the season again began on the first Monday in April (the 2nd).
Cover only shown for the Northern section.
These are the latest releases I've come across, so it is unknown whether the ticket was available in 1964.
Here are some sample tickets (showing both sides). They were valid on all regular and excursion steam diesel and electric trains:
The tickets were not marked as northern or southern, but had the area they were valid in defined. North was Alnwick, Carlisle, Penrith, Kirkby Stephen, Richmond, Eaglescliffe, Middlesborough and Whitby. South was Whitby, York, Harrogate, Ripon, Skipton, Hebden Bridge, Marsden, Denby Dale, Barnsley, Cudworth, Bolton-on-Dearne, Doncaster, Goole, Hull, Hornsea and Withernsea.
Diesel Passenger Trains (Timetables) 1956 - 1960
Diesel Trains (brochures) 1956 - 1960
Day Line Diesel tickets 1958 - 1963
Timetables, posters and brochures
Edinburgh Suburban Service timetables 1958 - 1963
Local Services - the new image (refurbishment, BRB 1974)
Many timetables can also be found on the Regional pages of the Operations section.