I'm a reporter on a 'local rag' 
Firstly, the paper has the right and responsibility to publish details of all hearings in court to ensure the principle of open justic is upheld. It is a vitally-important tenet of our legal system and slagging off reporters for publishing details heard in open court (including coroners' court) is perhaps not the way to solicit good advice with regard to your problem.
As for your question, there is a mechanism by which your friend could seek an order banning his address from being published. He would need to seek a section 11 order (through his solicitor. I would not recommend him trying to do it himself). Note that if a press reporter is in court they are very likely to oppose the order.
Discretionary reporting restrictions are only imposed by the court in rare circumstances, based on clear and cogent evidence, and as a last resort. I've not seen many made, but it very much depends on which magistrates are sitting that day.
The guidelines (Reporting restrictions in the criminal courts 2014) state that an order should not be made for the comfort of a defendant, but only where there is an evidence-backed risk of serious injury or death from reporting the address (in this case) of the defendant.
These are the relevant paragraphs you need, but the whole document is online should you wish to read it. If I were your friend I would keep my fingers crossed there are no reporters in court to oppose the order.
"Consistent with the requirement to protect the open justice principle and freedom of expression, courts should only make an order under s.11 where the nature or circumstances of the proceedings are such that hearing all evidence in open court would frustrate or render impractical the administration of justice.62 It follows that a defendant in a criminal trial must be named save in rare circumstances.63 It is not appropriate therefore to invoke the s.11 power to withhold matters for the benefit of a defendant’s feelings or comfort64 or to prevent financial damage or damage to reputation resulting from proceedings concerning a person’s business.65 Nor can the power be invoked to prevent identification and embarrassment of the defendant’s children, because of the defendant’s public profile.66
Where the ground for seeking a s.11 order is that the identification of a witness or a defendant will expose that person to a real and immediate risk to his life engaging the state’s duty to protect life under Article 2 ECHR,67 the court will consider whether the fear is objectively well‐founded.68 In practical terms, the applicant will have to provide clear and cogent evidence to show that publication of his name will create or materially increase a risk of death or serious injury.69"