Both teams lost their opening games of the tournament last weekend to Ireland and France respectively.
Despite England coming into the game as heavy favourites, Hamilton believes that the hosts are capable of making life difficult for them.
"There's no two ways about it, it'll be a tough game," he is quoted as saying by Sky Sports News.
"It's always great to play at Murrayfield in the Calcutta Cup match and what positives we can take out of that game we'll try and do so.
"It's a cruel sport and with Scotland over the last few years it has been tough. We're used to having disappointments but then bouncing back. We're well capable of running out a huge performance on Saturday."
Scotland have lost their last four encounters against old rivals England.