Cheques are a powerful tool. They enable 'people', non-banking enteritis or non-states, to 'create' money - just on the power the note/cheque promises to fulfil. If someone you trust enough offers you a 'post-dated' cheque you prospectively will accept it; if that is in your interest. This could be done with a simple letter - effectively a promissory note - but with a cheque the simple mechanism is in place to easily realise the money - pay in into your bank and draw cash - whenever the date and payee name is valid.
In theory people could use trusted 'open' cheques (with no payee named and maybe undated) to trade and barter without paying the cheque into a bank, just so long as the cheque's issuer is trusted by each party who in turn accept it (effectively a demand promissory note). This indeed once happened with counter-signed Banker's Drafts, they would often change hands until banks started to refuse to accept the counter signing as valid (on grounds of fraud prevention) and now do not issue drafts at all.
If the next step of government is to remove 'cash' from society and use various auditable and identifiable means of electronic payment devices in its place, that is all fine-and-dandy apart from for the black economy - transactions that are done 'for cash'.
With the advent of 'digital cash' what will replace paper-money/cash in the black economy? Gold? Bags of dope? Signed cheques from enteritis who have an established creditworthiness (trust) in the public mind?
Call me suspicious because I do suspect there is an underside to this motion: to end the use of cheques. And I suspect my synopsis above is not so far from that truth; that it is all about making people find tax-avoidance progressively harder to carry-out. (and bank cashless-transaction charges no doubt).
See: Promissory note - From Wikipedia
See: Bills of Exchange Act 1882
An example of a 'trusted open note/cheque' would be shopping vouchers for say Tesco or Waitrose, postage stamps, etc. I would accept a few of those right now.
See: Is a cashless society on the cards?
On the other hand; the people will do much better to revert to our own form of currency. Since our money already is not actually issued by government at all; it is all raised through the banking system and is 'taxed' therefore by interest charges and inflation (a 'tax' that goes directly to the issuing bank).
Gold is one option for underpinning state-free currency. Any number of trusted gold investment companies can sell paper notes (cash) which can be simply exchanged for real-gold - just like the old days - you can pay me with those!
But the gold market is still vulnerable to manipulation since the self-same bankers who create the money today also keep their wealth in gold and control the gold market.
Paper promise notes could replace this that simply represent one hour of work. A Doctor may charge ten units for one hour of medical advice, a night watchman may charge half a unit per hour for sitting keeping an eye open.
That is really what we all have for sale and by what everything is represented; human effort. Be it making something and getting it to the store or digging minerals from your land. All boils down to human effort.