<...an "open door policy.">

In this instance "open door" is an adjective modifying policy. As such it wouldn't require an article, but should have a hyphen: open-door policy.

Back to comparing Brit-vs.-US article usage: Here in the US we speak of a shop located "on Main Street." I believe the UK version would include the definite article: "on the High Street." I've heard people, both in Canada and the UK, speak of going to University. Why is it that USns go to college, or to a university?