You might be doing yourself a favour to be looking at public liability & fire insurance requirements as well .
As it is in a the national park you may well be on to a hiding to nothing .
I'd take the bull by the horns and write a letter to the planning dept asking for simple definitive a reply with chapter & verse references & for you look up & for you to have the reply in 30 working days . Send it in by recorded signed for mail ....... perhaps including in the letter .. " So you know if it is a sensible thing to consider proceeding with . Note Well you are not asking for planning permission or a planning consultation at this stage " .
Trying to get the info on official headed paper will mean that you'll know one way or another as cheaply as possible .
If they say No problems & their minds change with the weather you'll have the evidence you might need to help you .
If it's a No you won't have left yourself open to enforcement fines and other problems in the future.
I guess the same may apply if you said free parking but sold surplus honey , eggs and veg etc. or other things ( not grown / made specifically for sale .... making them garden gate sales ) at the field gate but it could be worth exploring /thinking about before you make any contact with the authorities .

Due to the number of foot falls going by , would you getting a working ice cream van help with earning money , you could then say seeing as you've purchased an icecream you can park here for nothing , to eat it and perhaps take a stroll around the area on the coastal path if you feel like it.
