Presumably passengers will change trains at Reading
Well yes, at the risk of stating the obvious, clearly most of the eastbound trains calling at Reading will continue to Paddington, and therefore Heathrow-bound passengers will need to change, but that certainly doesn't rule out at least some through trains to LHR from Bristol, Wales and the southwest.
Or, as FDF suggests,
via LHR - though it's not immediately obvious where they would continue to or what would be the point in that.