I recently booked a hotel on the LHR website (it's a bit clunky). The rate was the same for the IC Willard (same as the best flex rate). Strangely enough, at checkout, I was charged a lower tax % (something like 5%, instead of 14.5%). It was a very nice deal because the Willard does not have an exec lounge, or breakfast in lieu of it - and both it, and a $100 F&B credit, are included.
Unfortunately, I didn't get a "stacked" upgrade.