That would make it possible to record the stream. The UK legal system is very apprehensive of allowing any recording of what takes place in a courtroom that isn't filtered through a human observer's memory.
The audio is always recorded and transcribed at a Crown Court. The transcriptions are a permanent record. This is why for example if a witness nods to affirm something they'll be asked to actually say "Yes" out loud if that's what they meant.
You can fill out form EX107 to apply for the transcript of some particular trial or part of a trial heard. What if anything is available will depend on what your reason is for requesting the transcript and the nature of the case.
Unsurprisingly if you request transcripts of a case in which someone was accused of raping a child, the witness statement from the child and associated examination by counsel may not be available to satisfy your "idle curiosity" whereas they might be available to the defence lawyer for the accused who is appealing the sentence based on something said in that part of the trial.
In general the reporting restrictions in the UK are there because there has been a history of recordings leading to jury prejudice and therefore mistrials.