One of the most famous judicial statements throughout legal history was that of Lord Hewart CJ in Ex p McCarthy  1 KB 256 - ". . . it is not merely of some importance but is of fundamental importance that justice should not only be done, but should manifestly and undoubtedly be seen to be done."
In the House of Lords judgment in Abdroikof  UKHL 37 , Lord Bingham (at paras.14-16) noted that the test for bias had been developed through a series of cases. His Lordship said - "The legal test is whether the fair-minded and informed observer, having considered the facts, would conclude that there was a real possibility that the tribunal was biased. The characteristics of the fair-minded and informed observer are that he must adopt a balanced approach and will be taken to be a reasonable member of the public, neither unduly complacent or naïve nor unduly cynical or suspicious."
This recent blogpost - 'Fracking' protesters jailed ~ Public Nuisance ~ excessive sentences - looked at the sentencing, for public nuisance, of three men who protested about fracking operations at a Cuadrilla site in Lancashire. An appeal against the sentences has been lodged - The Guardian 5 October 2018.
It is now reported that a company (J C Altham and Sons)*, controlled by members of Judge Altham's family, supplies the Irish Sea oil and gas industry - Daily Record 11 October and Mirror 11 October. The article states that the company supplies "ships’ stores, including food and drink, tools, rigging equipment and clothes." The article does not state that the family business supplied Cuadrilla but the Centrica business (which includes British Gas ) is a significant investor in fracking operations conducted by Cuadrilla. As reported in June 2018 by Drill or Drop, Cuadrilla, "recorded an annual profit for the first time following a multi-million dollar payment from partner, Centrica."
There is a clear implication in the Daily Record report that there is an appearance of bias in the involvement of Judge Altham with the fracking protesters. The argument would run along the lines of the judge imposing heavy sentences so as to deter further protests because a business run by members of his family benefits from trading with companies involved in gas extraction / fracking.
This does not look good and the law extends to appearance of a real possibility that the tribunal was biased. It remains to be seen whether this is raised in argument at the appeal. The judge would have done well, in all the circumstances, to have recused himself. Strict avoidance of the slightest appearance of bias is a key factor in upholding public confidence in the fairness and impartiality of the judiciary.
Guidance for the judiciary is to be seen at Guide to Judicial Conduct - revised March 2018
* Two companies appear in a Companies House search - Mrs J C Altham and Sons (Lancaster) Ltd (described as Agents involved in the sale of a variety of goods) and Mrs J C Altham and Sons (Morecambe) Ltd (Production of meat and poultry meat products).
The High Court refused to grant an injunction to prevent fracking at Preston New Road - BBC News 12 October.
: Postcript :
At the appeal it was not necessary to hear argument about bias - see para 6 at Roberts and others v R  EWCA Crim 2739. Nonetheless, the court considered the point at paras 7 to 16. The court's judgment appears to lean against a finding of bias.