I'm not sure how to mark the clause boundaries

It might be helpful to split it into two sections; the initial large preposition phrase containing several sub clauses and functioning as an omissible adjunct, and the subsequent main clause with its own numerous SCs:

PP Adjunct

With [more than 430,000 migrants having reached Europe by sea this year], [the countries of Europe resurrecting borders [they'd once removed], and [thousands of people in Calais trying [to reach Britain illegally]].

The PP is headed by the prep with, which has as its complement 3 coordinated sub clauses, 2 of which contain further sub clauses:

1) more than 430,000 migrants having reached Europe by sea this year.

2) the countries of Europe resurrecting borders [they’d once removed], containing the relative clause they'd once removed which modifies the NP borders.

3) thousands of people in Calais trying [to reach Britain illegally] containing the clause to reach Britain illegally, which is catenative complement to trying.

Main Clause

[Some people have argued [that we're on the verge of a 'great age of migration' [in which national governments are powerless [to resist huge numbers of people, [travelling the world in search of a better life]]]]].

The MC contains 4 sub clauses:

1) the large that-content clause as complement to have argued, and containing:

2) the relative in which clause modifying the NP great age of migration, which in turn contains:

3) the infinitival to resist clause as complement to powerless, which contains:

4) the participial travelling clause modifying the NP huge numbers of people.

(note: some grammars would analyse the having in having reached Europe as a catenative verb with reached Europe thus a sub clause as catenative complement. To keep it simple, I've treated having reached as a constituent, i.e. 'the verb'.

Here is my effort to show the clause structure using indentation:

• With
  • more than 430,000 migrants having reached Europe by sea this year,
  • the countries of Europe resurrecting borders they'd once removed, and
  • thousands of people in Calais trying to reach Britain illegally,
• some people have argued
  • that we're on the verge of a 'great age of migration',
    • in which national governments are powerless to resist
      • huge numbers of people travelling the world in search of a better life.