It might work for the larger companies, but for the local windys that do mrs old neighbour and her friends, there is no chance this will work, and these are they guys that probably dont declare anyway.
On a personal note, myself and my missus are spending via cash transactions at the shops for food, clothing etc all paid for via cash we withdraw from the bank, it helps to have a physical feel for spending.
It allows you to keep better control of your finances without going into debt via CC or into an unauthorised overdraft using debit cards (my banks doesn;t always stop transactions, and if they do then i pay cash). Cheques can take time to get presented to the bank before they even clear so thats forgotton..
Paying by cash is the best method to prevent further dept of the general bristish public as a whole. It should be a better case for checking up what businesses receive by the IR, rather than stopping cash payments.