Eddie Jones' side go into the Six Nations match looking to equal New Zealand's world record of 18 straight Test victories.
However, Cotter says Scotland have enough attacking threats in their ranks to take the game to England.
"The players are keen when they get their hands on the ball to express themselves at Twickenham," said Cotter.
"I think that's a good attitude to have and attitude will determine a big part of the game.
"We know when we defend we'll have to defend resolutely."
Scotland sit third in the Six Nations table, having registered wins over Ireland and Wales either side of a narrow defeat by France in Paris.
The Scots, though, have not beaten England since 2008 and have the unenviable record of not winning at Twickenham since 1983.
Hamish Watson replaces the injured John Hardie in Scotland's only change from the win over Wales.
England have named the returning Billy Vunipola on the bench for Saturday's match, and Cotter admits the powerful Saracens number eight is just one of many strong options Jones can call upon late in the game.
"They [England] have a formula that is working well for them," said Cotter, who will be replaced by Gregor Townsend as head coach at the end of the season.
"They have a bench that is coming on and finishing games off in the last 10 minutes. It's something we're aware of.
"I think they'll comfortably move through the gears as the game goes on and finish in top speed and we've got to stay with them.
"We know more or less what's coming and it's just a matter of withstanding that."
Jones suggested in the aftermath of England's win over Italy that Scotland would be under increased pressure going into the Calcutta Cup match, with expectations raised among supporters after the wins over Ireland and Wales.
"Coaches have different characters and styles," added Cotter. "That's his and everybody has their own.
"I think Eddie's good fun, he's good company. I like having a chat with him outside of the game and in the game we both like to compete as best we can.
"Our players know they're going to have to give their best performance. During that 80 minutes we'll have to string together a number of excellent plays in attack and defence and to think clearly to get them to start adapting to our play.
"It hasn't been discussed a lot within the team, the Calcutta Cup, Triple Crown, nothing. All that has been discussed is content of the game and getting the content right. That's all this team is doing. Nothing else is being applied or talked about."
Head coach Vern Cotter insists Scotland are not going to Twickenham to merely try to contain England.