“The only evidence given by the prosecution was oral testimony.”
That’s usually the best type.
You need to separate the two issues.
Lying under oath (Perjury) is a serious offence. Accusing a solicitor (and possibly a judge) of conspiring to pervert the course of justice is a good step up from that. Concentrate on appealing your conviction. Get yourself a new solicitor, explain your concerns to her or him and demonstrate why you believe you have suffered a misjustice. Don’t worry about the alleged perjury and certainly don’t get involved with your conspiracy theory. Bear in mind that in every criminal trial the jury or magistrates will disappoint one side or the other. Just out of curiosity, was your case held in the Magistrates’ Court or the Crown Court?