It is clearly untrue that should asylum seekers stop in the first safe country they came to then the UK wouldn't ever take in refugees.
Clearly if any country neighbouring the UK had such issues, perhaps due to involvement in a war, or an inability of their government to treat the citizens with respect, then the UK would be a valid place to flee to.
In other circumstances there is no restriction on the nation getting swamped by genuine refugees on asking for help from other nations by their taking in a portion; but that is going through the correct channels not just invading and making demands.
And as in the present case of Ukraine we see the nation is perfectly capable of offering shelter to further away nations if it feels it is appropriate.
However a nation can not be Lady Bountiful, as a massive influx into an already overcrowded nation is sure to ruin the economy created here for all existing citizens, which is unacceptable virtue signalling (which probably seems attrack to the woke).
This is why, while one might have sympathy for those in a nation that seems to offer little to the masses, economic justification is not an acceptable excuse (and why it's rarely admitted to). We have a foreign aid system, we are willing to help others build their own nation, but we aren't obliged to cope with the result of other governments failing to put their nation on the right track.
Nations desire independence so then they need to accept the responsibilities that entails and listen to good advice on how to deal with issues. Letting the country go to pot to make the leaders wealthy is a ridiculous type of independence, and it is situations like that which the troubled country needs to sort; not simply let their citizens leave to impose themselves elsewhere where they are simply a burden; and a burden of thousands and thousands at that.