Beware how you go with this! Simple statements on this site (and others) such as “insist on proof” are sometimes less than helpful.
Firstly, a practicality. The idea of a fixed penalty offer (FPO) is for the registered keeper (RK) (or somebody who he nominates as the driver) to accept guilt and incur a reduced penalty. The paperwork sent with a FPO asks the RK to either accept the fixed penalty himself or to nominate a person who was driving at the time of the alleged offence. The RK has 28 days to respond to this request. Although some may do so, there is no obligation for the prosecuting authority to enter into any correspondence or to provide any information or evidence. The danger is that if you fanny about asking for this and that you may exceed the 28 day limit. The prosecuting authority may get fed up and may find yourself facing a S165 prosecution (failing to provide driver’s details). This is a more serious offence (minimum six penalty points) and is not too difficult to prove.
To move on, if, before deciding whether to accept the FPO, you ask for the calibration certificate and they refuse you will have to opt for a prosecution and you will have to plead not guilty to speeding in court. Before trial day there will be a “case management” hearing and at this you will be asked to provide the basis for your not guilty plea. You are not obliged to do this but if you “hijack” the prosecution by revealing your defence only at the trial the prosecution is entitled to ask for (and will probably be granted) an adjournment to enable them to produce the documents needed to rebut your defence.
At the trial the prosecution will state your alleged speed to the court and say that it was measured by a mobile camera. (They will probably give some details of the location and camera type and some other details to support their allegation). The onus then shifts to you to prove that the camera was inaccurate (which you will have to do to the lower standard of “on the balance of probabilities“). You may be able to convince the court that the camera may be inaccurate because it had not been calibrated for a while (if indeed it had not) but you should not depend on it by any means. You will almost certainly be required to show some other evidence to cast doubt in the Magistrates’ minds that your speed was inaccurately recorded.
You may be successful in securing details of the calibration certificate before any of this takes place, in which case all well and good. But if you do not it may cost you dearly. It is not a simple matter and unless you are genuinely not guilty (i.e. you were not exceeding the speed limit) the risk you are taking (of a higher fine as well as prosecution costs) is, in my view, not worth the effort.