they won't accept any reasoning for non guilty plea?
Who is 'they'? The court or the Police?
Right now they have no evidence you were driving so the speeding charge will fail unless you plead guilty to the charge, that would be a bad idea unless it has other benefits (see below).
Without some meaningful detail from you it looks likely you were guilty of the failing to furnish offence.
HOWEVER that offence carries more points and a much bigger uplift in insurance premiums so is to be avoided if possible.
IF (and only if) you believe it was probably you driving then the usual recommendation is to do a 'plea deal' where you offer to plead guilty to the speeding if the FtF is dropped, this is routine and always (if put properly) accepted, in fact there is little reason for them to dual charge you other than to make the deal easier.