Cash Businesses

Just a quick question.

For small businesses, running as sole traders, is there any legal requirement to deposit all cash receipts into and make payments from business bank accounts?

I went to 2 high street banks today and got completely different answers. One said that it is illegal to not deposit cash into the bank account, but I have doubts, I suspect that they would want me to put the money in considering the amount of money they charge for 'looking' after my money. The other bank said that there is no such requirement.

I run a small business taking primary cash receipts and a few cheques every now and then. I pay for purchases by cash with a few expenses such as utility bills from the business account. I usually keep a steady float in my business bank account to cover these expenses, but I don't normally put all income into the bank. The remainder of my 'drawings' I either hold in cash, put into a personal account or spend it. All the money I have left over is mine, being a sole trader.

I don't think I will need to prepare detailed accounts, but I do have a qualified accountant to do my books for me. I do keep adequate records of all sales and purchases and I pay the right amounts of taxes on my business income. I have ran this system for a few years and the accountant did not even suggest that there is something wrong with this arrangement. I am just a bit confused with what the banks are telling me. It would be rather tedious if I am to deposit money into the account and make withdrawals for every small business transaction. 

Want another opinion to see if I am missing something. 

Thanks in advance.