I don't think it's true that there's very little we can do. For example, I think one of the reasons people claim asylum in the UK is that their claim is more likely to be accepted here. Someone published data on this not long ago. I can't find it now so the exact numbers may be slightly off but I think in France they accept something like 25% of asylum claims while in the UK it's more like 75%.
The French have also shown they're prepared to ignore the ECHR. Late last year the French government wanted to deport an Uzbeki known as "MA", who is a radical Islamist and had already been refused refugee status by Estonia. The French government was told by the ECHR they couldn't deport him but they ignored the order and put him on a plane anyway.
So, if you're a rational human being who wants to claim asylum would you try your luck in France, where you have a lower chance of success and run the risk of being deported, or would you head for Calais and try to make it to the UK?