Actually, the French law against collecting race statistics applies exclusively to the government.
Any company could theoretically ask for its employees origins, though it would then have to be very careful not to give any hint that it might take any kind of discriminatory action from this data. It's hard to think of a reason that would make this data useful to a company anyway. But private statistics institutes do collect it. Also, the government does have data regarding foreign citizenship and place of birth of immigrants, because that's not racial data.
I don't think alextgordon was talking about law. I think he was saying that UK companies (just as French companies) would simply not care about collecting this data.
Anyway... I realise the historical and cultural context is very different between UK/France and the US/Canada, but I think our approach of race is widely better. For an anecdotal data point, my wife is Canadian, and Asian. When we lived in Montreal every encounter with random people seemed to be an occasion for them to ask her "where she comes from", with a slight frown when they heard "Montreal" as an answer. People would talk to her in English, and to me in French. It felt strange to me and a bit weary for her. We live in France now, and where she comes from is a topic that never comes up, the last time it happened was with Flemish tourists. My parents didn't ask either at the time, they just assumed she was from Canada and most importantly that it was none of their business. I like this attitude.
France has that law, not the UK. And the safest (legally) kind of bias is definitely the bias that is undocumented.