The best rule is common sense; if you're going to be operating in an area likely to conflict with any of our traffic, then give us a call. I would go for within 5 miles of the zone laterally (or at any time when "under" controlled airspace in the vicinity of a CTR as you describe) as a good rule of thumb.
And don't be afraid to call if you're further afield - if we're too busy we'll tell you, but I think that most approach units will do their best to provide FIS as far as their workload allows.
This probably isn't the case in the London TMA, but I'll let those better qualified in that area field that one....