Hcfyk

I have a table with two columns and 12 rows.
I require the table to appear on the left hand side of the page (which I can do), however, the caption is centered on the page.
I would like to place the caption underneath the table, and have it centered underneath the table.
The output is shown below.

documentclass[12pt,english]article
usepackagecaption
begindocument
 begintable[H]
 begintabular
 hline 
 Year & Population (millions)tabularnewline
 hline 
 $1900$ & $1650$tabularnewline
 $1910$ & $1750$tabularnewline
 $1920$ & $1860$tabularnewline
 $1930$ & $2070$tabularnewline
 $1940$ & $2300$tabularnewline
 $1950$ & $2560$tabularnewline
 $1960$ & $3040$tabularnewline
 $1970$ & $3710$tabularnewline
 $1980$ & $4450$tabularnewline
 $1990$ & $5280$tabularnewline
 $2000$ & $6070$tabularnewline
 hline 
 endtabular
 raggedrightcaptionWorld Populationlabeltable1
 endtable
 enddocument

Here is a way (since you already want [H] option and have loaded the caption package I suppose it will be ok for you):

documentclass[12pt,english]article
usepackagecaption
usepackagearray
begindocument
 % A noindent is possibly needed here as @Mico suggested in his comment
 noindentbeginminipage0.35textwidth
 centering
 begintabular
 hline 
 Year & Population (millions)tabularnewline
 hline 
 $1900$ & $1650$tabularnewline
 $1910$ & $1750$tabularnewline
 $1920$ & $1860$tabularnewline
 $1930$ & $2070$tabularnewline
 $1940$ & $2300$tabularnewline
 $1950$ & $2560$tabularnewline
 $1960$ & $3040$tabularnewline
 $1970$ & $3710$tabularnewline
 $1980$ & $4450$tabularnewline
 $1990$ & $5280$tabularnewline
 $2000$ & $6070$tabularnewline
 hline 
 endtabular
 captionoftableWorld Populationlabeltable1
 endminipage
 enddocument

Since the tabular material must be typeset flush-left (aka ragged-right), I think the caption would look better if it, too, where set flush-left. (However, see below for a different solution.) One can achieve this formatting objective by loading the caption package with the options singlelinecheck=false and justification=raggedright.

documentclass[12pt,english]article
usepackagearray,caption
captionsetupsinglelinecheck=false,justification=raggedright
begindocument
begintable[ht!]
 begintabular
 hline 
 Year & Population (millions)\ hline 
 $1900$ & $1650$\
 $1910$ & $1750$\
 $1920$ & $1860$\
 $1930$ & $2070$\
 $1940$ & $2300$\
 $1950$ & $2560$\
 $1960$ & $3040$\
 $1970$ & $3710$\
 $1980$ & $4450$\
 $1990$ & $5280$\
 $2000$ & $6070$\ 
 hline 
 endtabular
captionWorld Populationlabeltable1
endtable
enddocument

Alternatively, if the caption must be centered below the tabular material and the tabular material must be typeset flush-left, I suggest you (a) run captionsetupjustification=centering, (b) load the threeparttable package, and (c) encase both the tabular environment and the caption statement in a threeparttable environment. This setup allows LaTeX to measure the width of the tabular material and to center the caption below the tabular; if needed, LaTeX will automatically insert line breaks in the caption. This behavior is shown in the following screenshot.

documentclass[12pt,english]article
usepackagearray,caption,threeparttable
captionsetupjustification=centering
begindocument
begintable[ht!]
beginthreeparttable
 begintabular
 hline 
 Year & Population (millions)\ hline 
 $1900$ & $1650$\
 $1910$ & $1750$\
 $1920$ & $1860$\
 $1930$ & $2070$\
 $1940$ & $2300$\
 $1950$ & $2560$\
 $1960$ & $3040$\
 $1970$ & $3710$\
 $1980$ & $4450$\
 $1990$ & $5280$\
 $2000$ & $6070$\ 
 hline 
 endtabular
captionWorld Populationlabeltable1
endthreeparttable
endtable
enddocument