I have to say I wonder if said MP was correctly quoted because I think it much more likely that the UK reporter seized on the UK's fobia-ridden reaction to ID cards whereas he very possibly had a national register in mind. On that assumption I am convinced the French MP was correct. ID cards are not really the point - a national register makes it possible and very easy to get a card for your convenience if you want, where national registers exist it is not necessarily compulsory to have an ID card.
My son recently moved to Denmark and it took him just over an hour to complete his registration there, about forty five minutes of which was waiting his turn at the office in question where he was signed up to a GP as well. Upon registering he is also on the tax collector's books. Armed with his registration details he completed his rental contract (open ended with the rent increases listed for the coming decade and more), established his bank account, utility contracts, etc., etc. all in the space of another hour or so. Conversely, without his registration he could do none of these things, even as a non-resident he would have to register to get a job, a bank account, etc.
In the UK there is no national register and completing the above things takes an inordinately long and tedious process relying on such prosaic things as utility bills (a bit of the chicken and egg sometimes), etc., etc.
The UK is a disjointed administrative mess because it has never tackled its problems head on, instead relying on patchwork incremental solutions (the sticking plaster approach) until the next detail becomes a screaming problem and then applying another plaster. Since Denmark (which has a national register) outperforms the UK (which doesn't have one) on pretty much every worthwhile criterion, having a national register is certainly not causing harm - and people there certainly feel every bit as free as anyone in the UK. By comparison the discussion on immigration into Denmark is very straight forward and does not take place in the same fog and guesswork, where the facts are vague/unclear, massaged and disputed in every political direction, as in the UK.