Analysis

When comparing 23andme to census records:

By census breakdown through 5 generations (32grandparents)(~200 years)
23andme

As you can see the numbers arent quite exact. British & Irish is 52% vs 33% and French & Germany is 45% vs 39% (Later numbers being 23&me). This could be explained by people migrating prior to the 5 generations studied. For example, some English ancestors might have only lived there for a short period prior to 5 generations.

Full Analysis