Scotland recorded their first win of the current RBS 6 Nations Championship campaign at Murrayfield, but almost threw it away with a lacklustre second-half display.
Very few believe Scotland can dent the Auld Enemy's relentless pursuit of the Grand Slam and their coach fears the worst if they suffer a similar lapse in concentration.
"I've said all along that we will be competitive," said McGeechan. "We had a good hour against England here last year.
"We played well in certain areas but England, like France, if you drop off the pace or the concentration goes they have quality right through the team that will kill you.
"What we have to do is play with that concerted focus to make them work and play under pressure for the whole 80 minutes.
"With the plusses of the first half against Wales we have to take that on and put as much pressure as possible on them."
McGeechan wants his side to learn from their second-half lapse against Wales, but he fears they lack the mental strength to trouble England at Twickenham.
He insisted: "We have to look quite critically at ourselves in the second half because some of that was down to us as much as Wales.
"I want them to force sides to play under pressure for as long as possible."