Whoa!
Now that I've looked at the chart and you say there's no mention of an initial altitude on Clearance Delivery, I'm back with you Togalk. ( word of caution, as my location indicates, I'm not a LGW Dep controller)
Definitley climbing to 6000' in my reading of it. You may have a ROC that means you never level at 4 so that restriction would be obviated.
These are restrictions/requirements not cleared levels in my book. You most definitely ARE climbing to 6000'.