Sorry, I thought I said, "Anticipate a CLEARANCE not above 1000ft..." in my post, implying that an ATC CLEARANCE is required, and maybe triggering the idea in the pilot's mind that he must obtain a CLEARANCE to enter the London CTR! Must be mistaken!
Two further points : although only 800ftish AGL, there are plenty of clear areas on the BUR - ASC route for emergency/precautionary landings, as was evidenced by one of our Thames/SVFR Controllers who developed a rough running engine recently! Also, White Waltham is an option, Windsor Great Park etc.
I would suggest that on balance you are more likely to get ASC - BUR, than the Lee Valley routeing, especially if City Airport is open. Although at 2400ft you have greater decision time, the options for a forced landing are much more limited as the area is much more congested. This topic has been discussed recently on here; also see last month's GASIL.