The source If anyone is interested to read more:
http://www.cnbc.com/2017/06/26/barclays-bitcoin-regulators-fca.html
I sadly don't believe that the banking system will ever adopt bitcoin, If they start doing so, It would be for a particular reason they hide (most likely to eventually control bitcoin). The maximum that could happen right now is making bitcoin legal in some countries.
They are not likely to use actual bitcoin, more likely just a blockchain implementation to reduce their costs.
I would even argue it may be irresponsible to run a banking system on the public chain.