Since you say this is next to the lawyer's name, it presumably refers to the lawyer (which in the Crown Court means a barrister) and not to the judge. So I don't think J means judge here. I think it means junior counsel.

In the UK and Commonwealth countries, a lawyer who argues cases in court is a barrister (though nowadays soliciters can also act in court in certain cases). Barristers are of two kinds: junior counsel and QCs. When a barrister is "called to the bar" (in effect licensed to work as a barrister), he or she is a junior counsel. Then after 15 years or so of practice, barristers can sometimes become Queen's Counsel (QC), though by no means all of them do; most remain as "juniors". So junior doesn't necessarily mean young.

QCs appear in important or complex cases. When they do, they are "leading counsel": they take the leading role, with one or more junior counsel assisting them and following their instructions.

If the case requires more than one barrister, but a QC is not instructed, one of the junior counsel will be the leading junior, taking the leading role like a QC.

And in other cases, one junior barrister can act alone. I think this is the case in your document, and is what "J alone" means.

"Cases conducted as leading and junior counsel alone include:
R v Talbot – Murder of father by his son [...]"
http://www.1highpavement.co.uk/barristers/james-thomas/

"Mr Justice Henderson noted that: “Prudential was represented at the hearing by junior counsel alone, Mr Jonathan Bremner, who performed his task with conspicuous ability” "
https://www.pumptax.com/barrister/jonathan-bremner/

https://en.wikipedia.org/wiki/Junior_barrister
https://en.wikipedia.org/wiki/Queen's_Counsel