The House of Lords still has to agree to the law, but this is bound to happen.
Is it? The Lords (including right wing Conservative peers, like Michael Howard, a former leader of the Conservative Party) are very unwilling to break international law, as the government discovered over the Northern Ireland Protocol.
Everyone here (including, I would imagine, HMG) is expecting the Lords to throw out the bill, or at least its most objectionable aspects, meaning it can't be re-introduced for a year. That would effectively kill it, since it would run into the General Election.
ETA: The background to this is that, because of the long delays to lorry traffic caused by Brexit, asylum seekers no longer arrive invisibly on the back of lorries and slip away into the Kent countryside but arrive very visibly in small boats. Furthermore, since we're no longer in the EU, it's far more difficult to send failed asylum seekers back to EU countries they travelled through than it was before we left (this was pointed out at the time, but no one seemed interested, because unicorns, and anyway they'd had enough of experts).
The government rather rashly -- well, rashly if you believe promises should be kept, which Boris Johnson obviously never did, and neither do a lot of his colleagues -- to reduce immigration, both legal and illegal, and both have gone up since Brexit, so their answer to illegal immigration is to show their supporters they're doing something about it by introducing a law that they know has no chance of getting through the Lords, but that doesn't matter, because come the next election, they'll be able to say "We tried, but the lefty lawyers, judges and the woke House of Lords wouldn't let us."
Then, they hope, as does everyone else, they'll lose the election and it'll all be someone else's problem.
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