You are looking at this in a very simplistic way...
The Dublin Regulation - and our loss of access to it - is only one of the factors.
The Dublin Regulation allows EU countries to return unsuccessful applicants to other EU countries. The numbers of returns were always fairly small and it's not a particularly effective tool. That said, it is a not-particularly-effective tool we have lost access to. Perhaps more significantly (and it is difficult to quantify the effect), the fact that we can't return applicants to EU countries as easily is believed to be contributing to the influx.
But, in additional to losing access to the Dublic Regs, we also lost access to EURODAC - which now means that instead of quickly finding that an applicant had a failed application elsewhere in the EU, we have to assess them from scratch. That - and the growing backlog arising from it - means a significant increase in missed deadlines for deportations.
And the loss of access to treaties with third countries is also a result of Brexit. As an EU member, we had access to treaties with Pakistan, Bangladesh, Sri Lanka and other non-EU states, allowing for successful returns at a significantly higher rate than we are now able to secure - because we haven't been able to negotiate similar agreements to replace them (outside of the bloc, we simply dont have the same bargaining power).
All of those issues stem from Brexit and are significant contributors to the current crisis.
The EU has successfully tightened up its borders in recent years - as a member, we would have benefited from that. As a non-member, it drives more asylum seekers to us.
Again- thanks Brexit!
And yes - the EU's tightening of its borders has led to an increase in death in the Mediterranean and other areas (as more dangerous crossings are attempted) but we're talking about an increase of deaths in the 100s in 2024 - that does not explain how the EU was able to reduce asylum applications by almost 1 million.
The EU appears to be getting its asylum seeker crisis under control - and that's now bad news for us.
So yeah - zeroing in on just the Dublic Regulation is daft - its a small peice of a much wider picture of How Brexit Lost Control of Britain's Borders.