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Ofc, Appeals process is fundamental right of every convicted citizen.
A central pillar of our system.
There's the old joke about inmates. Half the inmates ' say they are wrongfully imprisoned, the other half have found God' ( It's a joke not a fact, clearly there will be a number of genuinely innocent people in prison and naturally a number accepted their guilt and moved through the parole process to release )
Automatic right to file, but not to be 'heard' ( It doesn't mean that the thousands of appeal proformas completed in prisons across the land will actually have any basis for the appeal to be heard.) IIRC she has 28 days to file and then she needs leave to appeal to the Court of Appeal is required. Her next ( new?) lawyer will assist LL and advise whether she has a basis. I didn't follow the LL trial but some of you who did might have had a hint of direction from her Defence during the past 10 months.
Filing an an appeal does not equate to having grounds for it to go forward.
As another WS member just posted, once LL appeals ( I think she's likely to try based on her past behaviour) a ton of people on MailOnline will pipe up ' See! Told you so. That means her conviction was wrong.'
( same reason I was advocating for a UK ' LawTube.' UK mass media not great at covering law here. We aren't born with knowledge of the basics, we have to pick it up.Most of UK's successful appeals are for non-criminal matters, Magistrates Court.)