Why does "numbers of people" take "has" not "have"?
Expenditure on direct payments has risen as numbers of people
using them has increased and now equates to £1.1 billion or
6% of overall gross expenditure for adults.
Source: An overview of the UK domiciliary care sector February 2013 PDF file
Our freedoms are being forfeited as our numbers grow. Quality of life
is reduced as numbers of humans increase.
Source: San Francisco Chronicle, EDITORIAL; Pg. 6; Letters to the editor; via COCA
Edit:
Grammar Glitch Central's take on “Numbers of participants has…?
Edit: more examples
Two Medway Grammar Schools, Chatham Boys and Chatham girls have over a
hundred spaces between them, as numbers of children in Medway drops
sharply.
Source: Grammar & Non-selective oversubscription and vacancies, in Kent & Medway secondary schools
In both cases, divergence from the 7:3 ratio will be deemed to be
drift, in retrospect at least, if the divergence declines as numbers
of tosses or generations increases.
Source: Darwinian Reductionism: Or, How to Stop Worrying and Love Molecular Biology, Alexander Rosenberg, 2008 via Google Books
Best Answer
Maybe there is a difference here between American and British usage.
In America, we would say "The number of people has increased." (Omitting all the irrelevant parts of the sentence.) Then it makes sense: "number" is the subject of the sentence, and "number" is singular. There may be a million people, but there is only one NUMBER of those people. Thus "the number has increased". A singular subject with a singular verb.
I don't know if the usage in the UK is different, or if this was a mistake in the original document.