I’ve lost my digi card. Very embrassing I know 
but now I don’t have 28 days of records on me! Is there some form of dispensation, or would VOSA just be reasonably understanding.
You probably know that you have 7 days to report the lost card but to be honest I’d report the card lost and order a new one immediately as you only have 15 days to get it.
I can’t see you having a problem with VOSA especially when the card is reported lost 
You probably already know this but when you drive without the card you should take two printouts, one at the start of the shift and another at the end of the shift.
On both printouts you should write your name or driver card number or driving license number (which is likely to be the same as the driver card number) and sign the printout
You’ve reported the loss so if you get stopped it will be a matter of record as to why you cannot produce all the required records and only have those you made via the printouts since the loss. Nothing to worry about.