I came across this phrase around 20 years ago, and have always understood it to mean 'most of'. I might complain about having to pay "the thick end of £4" for a coffee, when it cost somewhere between £3.00 and £3.99. That meaning sounds fairly obvious to me. I'm in the UK.
Imagine my surprise when I used it in company recently, and it was interpretted differently. That a "journey would take the thick end of 9 hours" was received as not as the "around 8 hours 45 minutes" that I meant, but as "over 9 hours, possibly a lot over". Is this reasonable?
I have looked on the net, and the best I can come up with was this (right at the bottom, References in classic literature) which has many examples, but still no definition.
Can anyone find a published definition, an argument for what the interpretation should be, or at least moral support for my interpretation?