I would echo what an earlier person said, don't even think about using taxis or Uber, get the train from Waterloo out to Twickenham, the stadium is about a 10 minute walk away.
On the way back if you are out with the first batch of people & get to the station quickly & there is no queue then get in line & wait, if not & the queue is enormous, head for the platform with trains going away from London, get the first train & then get off at the next station, cross over to the platform with trains heading back into London & grab the first train.
I live to the West