Should asylum be restricted to neighbouring countries

100,000 asylum seekers a year is massive, especially when you consider the many countries one has to pass through to get to the UK.
The right of asylum is an ancient right to flee a government or ruler that persecutes you. It goes back thousands of years. In the modern era the UDHR says:
Everyone has the right to seek and to enjoy in other countries asylum from persecution.
The problem is that we have people who do legitimately need asylum, but rather than seek it in the first country they pass into which is safe for them, they choose countries where economic opportunities are greater – such as the US, UK, Australia etc etc. Now you can understand why they want to do this, but does a refugee have the right to choose any of 200 countries to move to, or is the right only to get asylum in the first safe country they travel to?
I think that it now has to be seen as a right only to the first safe country, not to any country they choose. I think developed economies should take in many refugees and asylum seekers – but they should not be forced to take in every refugee in the world that can get to their borders.