Given the complexities involved in the migrant situation, I doubt that Labour would be able to do very much different from the Tories, although they cannot admit that, or do anything except promise something different, in order to secure votes at the next election.
The major problem for any government, is the sheer volume of migrants, both already here, and expected to come.
Because of the complexities of Human Rights legislation, any government is obliged to feed and house such migrants, pending process of their asylum request, and then the inevitable extended appeals processes that tie up the entire situation for months, heading for years.
We cannot easily extricate ourselves from those governing laws, and even if we could, the sheer volume of applications, and physical presence of the migrants offering them, makes the entire situation competely unworkable.
With no interest from France in keeping migrants there, when they can simply wave them across the Channel, the influx of boats is only ever going to grow.
I honestly cannot see a solution to this situation that will be in place in the next decade, if not well beyond it.
What i can se far more easily, is that if Labour are elected, they will inherit the entire horrible mess, and be in exactly the same situation, with exactly the same legal and numerical constraints as the Tories before them.
That said, it will be interesting to see what 'promises' Labour offer to the electorate in order to secure votes.
Quite why any politician would rush to be in a government that has this to contend with, is a mystery, but that's politics - power is everything, no matter how impossible it is to actually use it effectively.