There was a time when they did man most border crossing points (major roads, railways etc) but once it became the EU, and border controls were dropped, they all went.
I guess there was always ways of getting across the border if you went via small lanes or even walked over fields, as you say, they cannot man every stretch of the border.
Of course it has always been possible to get into England with no passport via a boat into a small port, or even get dropped off by boat on a lonely beach.
If you think about it you do not need a passport to go from England to Scotland or Wales.
The idea is we make Europe the same, no passport to get from Spain to France or France to Belgium and so on.
The problem with this is that it opens up the door to illegal immigrants or criminals, once they get into Europe they can move fairly easily from country to country.
As we all know this has been a huge problem in the last 10 years and we are now stuck with hundreds of thousands of people inside Europe who have no right to be here, and we dont want, but cant get rid of.