I have been teaching monetary economics and money and banking for nearly two decades. Back in 1998 I gave a lecture on the future of cash and the possibility of a cashless society. In 2015, we are closer to having a cashless society than we were back in 1998 thanks to the likes of Google Wallet, Apple Pay, Bitcoin, and ubiquitous credit cards. However, we still use cash and lots of it. Why? Convenience, anonymity, and the grey economy go some way to explaining our demand for cash. The cost to small retailers of going cashless is also playing a role. However, a lack of trust in the security of electronic payments skews the preference of many away from e-money towards cash. In addition, many low-income families do not have access to electronic payments systems because they are unbanked.
The Bank of England video below gives an excellent overview of the future of cash. Will we be cashless by 2035? I for one doubt it.