https://fullfact.org/immigration/ref...-safe-country/

Not sure this is proof, but this is what I'm reading.

Refugees are not obligated to apply for asylum in the first safe country they enter. However, the UK is not obligated to consider asylum application even if they are in the UK.

That said, there is some UK domestic law which allows the government to refuse to consider an asylum application if it is judged that the person could have claimed asylum elsewhere.
Also

Although it’s certainly true that crossing the Channel without authorisation isn’t a legal way to enter the UK, Article 31 of the UN Refugee Convention states that refugees cannot be penalised for entering the country illegally to claim asylum if they are “coming directly from a territory where their life or freedom was threatened” provided they “present themselves without delay to the authorities and show good cause for their illegal entry or presence”.
Article 31 doesn't apply because they are not fleeing for their lives or freedom from France.

And none of this article deals with the problem of boats arriving at the English coast.

Those that succeed in getting here like this, well they're here, we have to take care of them, but we should be discouraging this method of arrival because it's extremely dangerous and unnecessary. There are better ways to apply for asylum in the UK.