Lord Thomas said that Sellafield deserved very considerable credit for the guilty pleas made at the first available opportunity and the very considerable co-operation it displayed after the discovery of the failures.
In considering the appeal, the court also took into account its previous offences.
The court had regard to its turnover of £1.6 billion - or £30.7 million per week - and its annual profit of £29m - or £560,000 per week.
Lord Thomas said It was clear that viewed in the light of those financial circumstances, a fine of £700,000 after a guilty plea was a fine which reflected a case where the culpability was moderate, the actual harm in effect nil and the risk of harm very low.
"A fine of the size imposed, even though only a little more than a week's profit and about 2% of its weekly income, would, in our view, in the circumstances achieve the statutory purposes of sentencing by bringing home to the directors of Sellafield Ltd and its professional shareholders the seriousness of the offences committed and provide a real incentive to the directors and shareholders to remedy the failures which the judge found existed at the site at Sellafield."
More top news
A report published on the first anniversary of Storm Desmond ranks it as the largest event of at least the last century.
Kerrie Gosney brings you Sunday night's forecast
From next week it'll be banned in Scotland. The legislation was put forward by former South of Scotland MSP Jim Hume.