After fruitless searching in the fora and much cursing and pulling of hair (something I can ill afford) I have discovered the following rules for specifying cart links messages, which I hope will save others the same grief.
1. To stop the default "xxx added to your shopping cart" message, use the specification "_m0" (NB the underscore). For example ...cart/add/p23_m0?destination=cart.
2. To insert your own message, first define your message in the Cart links messages panel on the Cart links settings page, by entering for example "99|My message text", then use the specification "-m99" (NB a dash, not an underscore). For example ...cart/add/p23-m99?destination=cart.
3. Note that just specifying "-m99" will display both your message 99 and the default message. If you want to display only your message, use the specification "_m0-m99". The _m0 must come first.
4. For additional messages, use dashes, eg "_m0-m99-m1337".