In reply to Jesus_C:
Thanks for the comments.
It turned out that you can pay with the app "JustPark". And you can pay for as long as you need for instance we paid for Saturday evening to Monday morning which meant three days.
It seems they have moved to this app recently.
I could download the app from there although the signal was poor.
This was for the National Trust car park.
Lake Head Car Park - Cars
Seascale CA20 1EX, Seascale, CA20 1EX
There was another carpark after this one, at the end of the road in a field with lots and lots of places. It was unclear if it was free or you had to paid to park there or just donate to the donation box.