Wow- I'm glad I emailed the concierge to ask my luggage question as I have no idea where this thread went. And just so people do know the answer to my question, they do indeed store luggage as they used to. I will drop my bag off on the way to Heathrow and pick it up when I arrive for my stay. That way I won't need to travel to Amsterdam with a big suitcase for just 3 days.
I've stayed at Sheraton Skyline many times over the years and wish they had a duplicate location IN London. They're very kind and quite helpful, and I've never had a bad stay.
As for cabs, I've also never had an ill-tempered cabbie in London. To the contrary, I've always enjoyed hearing what they have to say. Great hotel.