除了前面几位老师的翻译外，我觉得这个句子还有一种可能的翻译，即翻译成：他到伦敦还不到一个月就发烧病倒了。

这里的 scarcely 是修饰 a month 的，可以将 scarcely a month 译为“几乎不足一个月”。类似的句子如：

There were scarcely a hundred people present. 出席的不足一百人。

She had been in London scarcely a month when she was struck down by a fever. 

【翻译】她刚到伦敦才一个月就发烧了。

scarcely 的本义是表达“否定”概念。意为：“几乎不；简直不；决不；肯定不；肯定没；大概不；也许不”。但是用在复合句的主句中，例如：scarcely... when... 结构中，由于主句使用了“过去完成时”，说明早于从句的“一般过去时”。这时，scarcely 就没有了否定的含义，而表示“刚刚；才”，意思上等于only，just。网友的句子便是。

又如：

They had scarcely left the station when the train stopped.

Scarcely had they left the the station when the train stopped.

他们刚离开车站，火车就停下了。

She had been in London scarcely a month when she was struck down by a fever. (= Scarcely had she in London for a month when she was struck down by a fever.)

【翻译】她刚到伦敦才一个月就发烧了。

【说明】scarcely ... when [before] 的意思是“一 ...... 就”。例如：

The noise had scarcely died away when someone started to laugh again . 嗓音还没消失，就有人又突然大笑起来。 （摘自《外教社 .柯林斯高级英语用法词典》p.797,上海外语教育出版社2007年1月第1版）

He had scarcely gone into the room when [before] the phone rang. = Scarcely had he gone into the room when [before] the phone rang. 他刚走进房间电话铃就响了。（摘自《外研社英汉多功能词典》）

以否定词和半否定词开头的hardly...when, barely...when, scarcely...when以及no sooner...than等的倒装句式常表示“一......就......”。如：

Hardly had we started when it began to rain.我们刚出发,就开始下雨了。

Barely had the bulldozers started when Museum of London archaeologists swooped. 推土机刚一启动，伦敦博物馆的考古学家们就蜂拥而至了。

Scarcely had she entered the room when the phone rang. 她一进屋电话就响了。 

No sooner had he arrived in Rome than he was kidnapped. 他刚到罗马就遭到了绑架。

▲若否定词或半否定词不位于句首，则句子不倒装。