I don’t want to sound condescending but I don’t think you understand the reality of living in a nearer safer country.
So for an example we can look at Syria. Most Syrians will go to Turkey, where they’ll stay in temporary settlement camps. Turkey is not a rich country, and the camps are awful places with extremely basic provisions (clean water and a tent/hut). Some don’t even have electricity. There is a lot of anti-refugee sentiment, and the government are closing camps all the time. There are currently four million refugees in Turkey.
There are also two million refugees in Lebanon, out of a total population of less than six million. Over 1 in 3 people in Lebanon are refugees - mainly Syrian followed by Palestinians. And similarly, the conditions of the camps are squalid. There is no chance of a ‘life’ there.
That is why people try to get out, quite understandably. So the next safe country is either Greece (by dinghy) or Albania (via mountains). Both are impoverished countries. They can’t afford to support millions of extra people. So when they can’t get work or shelter there, they move on. And they’ll keep going until they can make a life somewhere.
It’s not fair to expect one country to absorb them all. One phrase that really gets up my nose is “But why do they all come here? It’s for the benefits!” They don’t all come here. In fact we take very few compared to many other countries. They actually get the same benefits pretty much everywhere in Europe. But if you’re English-speaking (as a lot of the world is) and have a cousin in the UK who runs a business and can give you work, then the UK would be a more attractive prospect than going to a country where you know nobody and can’t speak the language.
On the list of countries with the most asylum seekers per capita, the UK is in 58th position.