"There is continuing evidence of libel awards in sums which appear so large as to bear no relation to the ordinary values of life… It is in our view offensive to public opinion, and rightly so, that a defamation plaintiff should recover damages for injury to reputation greater, perhaps by a significant factor, than if that same plaintiff had been rendered a helpless cripple or insensate vegetable.”

This was the position of the court in John v MGN, when Elton John sued a newspaper for alleging he had an eating disorder. The court basically decided that even in cases of libel, where the damage is only to reputation, the same scale as that used in personal injury should be used - i.e. compensating for the loss. So if you lost your arm your damages would include medical bills but also your expected loss of earnings. In the case of reputation, the court will attempt to give a value to reflect the possible losses that will stem from it.

“In assessing the appropriate damages for injury to reputation the most important factor is the gravity of the libel; the more closely it touches the plaintiff’s personal integrity, professional reputation, honour, courage, loyalty and the core attributes of his personality, the more serious it is likely to be.”

All these comments were aimed at being instructions for juries, but the Defamation Act 2013 has since abolished jury trials in defamation suits. There hasn't been any significant caselaw on the issue since the new laws were passed but I would imagine the trend of keeping damages for loss of reputation low will continue. You might well be right that the financial value of Taylor Swift's reputation is far higher than the earnings potential of your arm, but the courts here have seem more concerned with the moral aspect of the decision... In the Elton John case the jury originally awarded over £300,000 in damages, and the court of appeal reduced it to £75,000.