What dialect/accent in the UK do people not say the word "the"
The is often reduced in Yorkshire dialect, to varying degrees.
It is most commonly reduced to an unreleased stop, usually glottal, but sometimes elsewhere in the mouth (eg "walk t'dog" /wɔkɂdɒg/ - there is usually no /t/ sound, despite the customary spelling).
But in informal contexts, this "catch" almost disappears, and it can sound like /wɔkdɒg/ "walk dog".
See this discussion in Wikipedia.