Sorry but I think David is correct.
First, if you read the Criminal Appeal Act 1995 carefully, you will note that no explicit statutory exclusivity is given to the CCRC for criminal appeals. In other words, there is nothing in that Act that says you have to go through the CCRC first.
Why, then, do people bother with the CCRC? Because of the Court's powers in section 5(1). As a practical matter, if somebody did try to appeal direct to the Court of Appeal, then the judges would almost-certainly invoke section 5(1) of the 1995 Act (which is section 23A of the 1968 Act it amends), which is the power to order that the CCRC investigate the case - effectively putting the matter in the hands of the CCRC anyway.
In view of all this, normally Jeremy would go through the CCRC, like virtually everybody else. However, David's point is that the Campaign Team claim to hold exonerating evidence. With such evidence, it would not be unreasonable for his Campaign Team to dispense with the CCRC and go direct to Essex Police or the CPS, or both, and ask them to consider their position on the basis that an agreed application could be made to the Court - maybe starting with an application for bail.
There is case law on this point arising from the joint enterprise appeals. A number of cases say that the Court of Appeal acknowledges its direct jurisdiction and that an appeal without the CCRC is permissible, though it is also stressed that this is rare.
The cases are R v Walsh [2007] NICA 4, Christopher Boughton-Fox v Regina [2014] EWCA Crim. 227 and R v Yassain [2015] 3 WLR 1571. In these judgments, the appeal judges are effectively rebuffing the CCRC. The Commission had always claimed an exclusive right of appeal in criminal cases once the immediate appeal period is exhausted (and the Commission still impliedly claims it has this right). The Court decided this is not the case, albeit that direct jurisdiction is to be exercised exceptionally.
None of this is to say the Campaign Team should follow the unconventional route, but as David rightly says, you have to ask, why mess around with the CCRC if there is evidence that exonerates Jeremy?