You do not have a case. We sometimes try the "legitimate expectation" argument for council PCNs, with some occasional success, but it has been specifically held that "legitimate expectation" cannot apply to criminal offences.
Your best bet is to take a driver education course for the first one and a fixed penalty for the second one, assuming you are eligible and are offered these options.
For what it's worth, "going downhill on a wide dual carriageway" is not really mitigation, it could be seen as aggravating: it could mean that you think speeding is OK in those circumstances, or that you are unable to control your vehicle properly when driving downhill.
Are there any issues with the signage?