Answer:
There isn't a direct one.
As you are travelling between airports, I assume you've got baggage and will want to avoid long esculators and stairs. I recommend you take the London Underground Piccadilly line from Heathrow (it doesn't matter which terminal you come from), change at Hammersmith for the District Line and head east, change at Westminster for the Jubilee Line and head east again, and then change for the DLR at Canning Town and catch a DLR train heading for Woolwich. London City Airport is served by trains on this route. All these stations have step-free access