My solicitor was useless from the outset (Legal Aid only promises a defence council, not that they will be in any way competent), he pretty much just stood for the start of the proceedings to give the "Not guilty" plea and then the rest was up to me. After all the crap I had been through (a couple months where the cops would arrive at my home and drag me off to the station at any time of day or night, keep me awake for a couple of days at a time and repeatedly threaten to ruin my life and the lives of my friends if I didn't roll over and take it) a £50 fine and 6 month suspended sentence was like a release from hell for a 16 year old me.
Appealing would have meant going through all of that again and depending on the judge I could have gotten an actual prison sentence, so no, no appeal.
I am actually quite grateful to the judge (Or magistrate whatever they're called in a magistrates court), he was quite scathing to the police officers (even going so far as to fine one of them for lying in his statements) and gave me the absolute minimum that he could under the rules of the court. He was convinced that I was innocent but because I could not prove it to the level required by the court he did what he could to minimise the sentencing.