AntiPolygraph.org's advice to anyone suspected of a crime has long been (and remains) to refuse any offer of a polygraph "test," to not speak with police at all (for reasons you'll find discussed here), and to retain legal counsel.

I think it would be prudent to discuss the questions you've posed here with your solicitor. However, if your solicitor advised you to submit to the polygraph "test," then I think you would be wise to find a better solicitor.

Although I'm not a lawyer, I see no reason why it would be in your interest to assist in your own prosecution by submitting to another interrogation (with or without the polygraph).

I don't know about UK law, but in the United States, while polygraph chart readings are generally not admissible as evidence in criminal trials, any statement made by the accused during a polygraph interrogation may indeed be admitted as evidence, and in some jurisdictions, polygraph chart readings, including a polygraph operator's accusation of countermeasure use, may be relied upon for sentencing purposes.