You can't appeal on the basis you did not have your case presented now to want to.
It would only be allowed if a conviction was 'unsafe'.
This is defined as being two areas:
a) error or irregularity of procedure
b) lurking doubt
These fall into further sub categories of
b) Inconsistent verdicts
c) Wrongful admission or exclusion of evidence:
d) Defects in the Indictment
e) No case to go to the jury
g) Inadequacy of legal representation
If you can satisfy any one of these grounds then you may have a case. Therefore you need to focus on these areas.
For more information please see:
That second one is very detailed guidance which you can read.
Can I clarify anything for you about this today please?