It's not like there are entire sections of the countries where you can't park at all. You just might have a 10 minute walk from where you can park.
That's actually far from true in many country places with narrow lanes, and usually no parking allowed on larger ones. One of the walks were doing quite locally, for which the picnic site car park is shut, theres a lay-by which fits 4 cars, another which fits 2 cars a few miles down the valley, one 0.6 km along the road from that which fits 2, and then a space which fits 2 but only if the first car parks tidily a few miles up the valley. There's nowhere else safe to park. This really isn't unusual.
Even when all the Lake District car parks are open it can be impossible to find a parking place for some walks if you're not early.
It may well be different in seaside towns... but if more of the residents are at home than usual there may be very limited street parking.