I have now looked at the data you suggest Keith. It is from ImmigrationWatch so may or may not be objective. However, while it looks arguably like a tracker effect from 1990 to 2007 (and not more recently) the immigration is bi-directionally countercyclical from 84 to 90, and untracking in 71/2, 73/4, 79/80, 81/82.

That could well be a happenstance correlation at most, like the legendary case of stork population and live births in Finland (sorry, I don't know the date but it is in all the student textbooks on statistics, or at least it was when I was younger).

Off the top of my head, what would the figures be if you tried to correlate (a) government in power and years from change with (b) net migration?