This time around however, they will face Saracens, who pipped Ulster to the last home quarter-final spot on the last weekend of the pool stages.
But Anscombe is undaunted by the trip and hopes Ulster's fans cross the Irish Sea in force.
"I'm delighted, it's an outstanding ground," he told the Belfast Telegraph.
"But more to the point is this - if we were at the Allianz Stadium with its 15,000, my understanding is that we only get 20 per cent of the seats.
"Now 3,000 Ulster supporters as opposed to 20,000, well? I think that's the key.
"It's a big occasion at a big rugby ground with a lot of history there so we can go and strut our stuff. More important than getting to Twickenham is getting to the Aviva (Stadium). But to do that, first we have to do the business at Twickenham."