With respect, Zulu, I feel you have missed the point entirely. The banks would still be custodian of your money, but it would be YOUR money and available on demand in cash. As I understand it, it would not mean you lugging suitcases of cash around, but would restrict banks' ability to lend beyond their means. Well, roughly that.
There was a good comment posted by the author, which I shall reproduce here:
At the moment, if you deposit money, you are lending the bank money. This comes as a surprise to many. Indeed our very own hapless former Chancellor of the Exchequer, Alistair Darling was always confused by this in his period of office, regularly referring to deposits as assets of the banks. They are liabilities from the bank to the depositors. The assets are the loans. This is “O” Level economics and accountancy. So, if cash is replaced (a virtually costless act by the government) and put in the depositors’ accounts and swapped for or converted the demand deposits and/or the demand deposits just cancelled, the banks would no longer owe their depositors anything. They would be custodians of their clients’ cash, with a fiduciary responsibility to protect it. Post reform, with no liabilities, a banks will only have its capital that started it and assets, i.e. its loan portfolio. So the net worth of all banks has gone up to the exact extent that the banks liabilities have gone down. Why make the bank shareholders suddenly £850 billion better off by this action on converting demand deposits for cash? I say do not let the shareholders have the £850 bn benefit; let those assets (the loan repayments) go to paying off the national debt.
As I said, I'm not sure if the idea is totally sound, but there are many advantages to 100% Reserve banking and, in these times of financial uncertainty, we need to think about making banking much more secure in the future. If the banks always hold depositors' accounts (unless you have opted to let them lend it for interest income) in cash equivalent, a run on a bank would be most unlikely. 
I feel you have missed the point entirely
Not for the first time

but it would be YOUR money and available on demand in cash.
Is that option not open to me at the moment?
it would not mean you lugging suitcases of cash around
I didn't envisage this when making the comment - rather - the suggestion (to me) seemed to place the money supply, as it pertained to the person on the street, in an every day fashion at least, firmly back towards hard cash rather than the electronic transactions now commonly used. :-/
Or perhaps the point of the exercise applies to what lies behind the counter of the bank on how the funds are accounted for and handled and has no relevance on how we go about spending it in the normal course of events. :-/ :-/

In any case, would properly constructed and enforced regulation not achieve the same result in terms of irresponsible lending and business practice by the banks? - As well as the depositors living within their means of course.
Finally, irrespective of whether or not deposits were held in cash, should sufficient people want to withdraw their funds, as a group, at any given time, would this not produce essentially the same result as a run on the bank?