That translates as the Saturday of the week before Easter (start of school Easter Holidays) to the end of the Autumn (Fall) school half term.
I can remember when the season was Good Friday and Easter week then May Day Bank Holiday to schools going back in early September, but it's gradually expanded.
The tourist gap after Easter no longer exists, and in September/early October it's the shoulder season when the weather is still good (everyone hopes) so you get the retired folk coming up to take advantage of the summer mobs having gone, more rooms and better prices.
And all the other tourist attractions still open as well.
Then mid to late October the families are back for one last visit of the year.
Buses like the 77/77A over Honister and the 508 over Kirkstone never used to run so early or late as the weather couldn't be trusted, but with global warming the chance of early fall snow disruption has now basically gone, as has the serious chance of any snow at Easter.
Now the 599 open top bus service runs 364 days a year- I was on it last year (wrapped up) at Christmas!!- unthinkable a very few years ago.