There is not a right to appeal as such, but you could bring an action in the High Court Chancery Division for proof of the codicil. Although its pointless if it wasn't witnessed, because it is invalid.
me me miss, I want to answer
( barmaid is the queen of equity both in the courts and AB - here)
you have a right to appeal - on anything
but in this case you dont have a hope
[ bit that is iffy -I think you can apply to the executor to give action to the obvious wishes - BUT it requires the agreement of all the beneficiaries, and if it is anything like my family, good luck with that]
Or do you mean that probate was granted to the unwitnessed codicil? (Which would be a very unusual mistake by the normally v efficient Probate Registry).