Because nowadays vast majoritie of „refugees“ are not refugees in a classic sense.

E.g. my country had thousands of „refugees“ hoping over border from Belarus last year. Last time I saw statistics, not even 1% was eligible for „refugee“ status. Even skipping the part that, according to international law, refugee is legit for the first safe country.

That last sentence is completely incorrect and is enough for me to safely disregard everything else you just said on the basis you don’t actually know what you’re talking about.

Even if some people try to challenge it and enable refugee shopping, calling it „incorrect“ shows that you don't know much about this topic.

It’s easy to prove me wrong: point me to the relevant lines in the relevant treaties or conventions that state this.

You can’t because they don’t exist. There is no obligation to seek asylum in the “first safe country.” This is a common trope trotted out by right-wing mouthpieces which is where I’m assuming you got the rest of your “facts.”

If you cross border illegally and don't ask for asylum, then you're, well, illegally crossing the border.

For EU, there's Dublin agreement.

Quote or reference the lines in the Dublin agreement that state this. Also, point out where IN U.K. LAW the Dublin agreement and these lines apply.

Your first sentence is irrelevant because this applies to refugees claiming asylum.