Uncontrolled mass migration (Thanks Tony Blair) under New Labour added five million people over a ten year period. Guess what, many drive cars. So yes, it has affected transport.
When I see people blame more drivers for traffic, the only culprit I can see is a failure to extend public transit accordingly. A huge number of people drive in New York, for example, for lack of a better alternative, not because driving is more convenient, cheaper, or in any other way better for them. Blaming car traffic on the number of people in a densely populated area is futile, and any place that has grown reasonably with its population has also abandoned the notion that cars should be the default mode of transportation.