The UK is not "enmeshed in the EU when it comes to human rights".
The UK is a contracting party to the European Convention on Human Rights, which was mostly written by British lawyers. This predates even the earliest precursor of the EU (the European Coal and Steel Community) and is overseen by the Council of Europe, a body that is completely independent of the EU and was not on the Brexit referendum ballot (and which was Churchill's vision for a "United States of Europe"). Every country in (greater) Europe is a member of the Council of Europe except for Belarus (which refused to abolish the judicial death penalty, a condition of membership) and Russia (which left just after the full-scale invasion of Ukraine, an hour before it would have been kicked out).
The European Convention on Human Rights doesn't have much to say about refugees/immigrants as such. It basically says that you have to treat all humans with a certain amount of dignity. Disputes about exactly what that entails are judged at the European Court of Human Rights, which again is not part of the EU.
The UK used to lose a lot of cases at the European Court of Human Rights because UK domestic law had never been updated to make it compatible with the European Convention on Human Rights. The Human Rights Act, passed by Parliament under the Blair government, fixed that, and now the UK rarely loses at the court.
There was a kerfuffle a couple of years ago when a bunch of people were about to be deported to Rwanda. Since they had different lawyers, some appealed to the UK Supreme Court and other appealed to the European Court of Human Rights. Contrary to what was stated at the time, the cases that reached the European Court of Human Rights under its urgent procedure did not result in the verdict that "The UK cannot deport these people". What the court said was "The UK cannot deport these people before they have exhausted all legal remedies in the UK, which means the Supreme Court". In those cases which went to the Supreme Court (rather than the European Court of Human Rights), the UK judges ruled that the deportations could not go ahead.
Thus, no European judge has ever actually made the ruling that Farage, Badenoch, and co would like you to imagine that they did. At no point has the European Court of Human Rights overridden a UK deportation order to Rwanda that had otherwise been validated by a UK court.
Where there is an EU connection in the story is actually the opposite of "still entangled". Before Brexit, the UK used to be part of the Dublin treaty, which made it possible for EU states to return asylum seekers to each other much more easily than is now the case.
The only thing in the international refugee law sphere that the UK is still signed up to is the UN Refugee Convention. Farage has said that a Reform government will either leave or ignore this. Thus, the stage will be set for the machine-gunning of the boats, which quite a lot of his supporters seem to dream of.
every time a new set of procedures are brought in to try and deal with the crisis they are thwarted by human rights lawyers
Lawyers are there to argue their client's case. They cannot "thwart" anything. Judges make the decisions, not the clients' lawyers, so if the judge says someone can stay, that's probably because the government didn't have a very good case under the law. Doubtless the Farage solution will to be portray the judges as "enemies of the people" (as the Mail did when the Supreme Court politely pointed out that some or other aspect of Brexit was illegal), and replace them with carefully hand-picked friends of the authoritarian government. We've seen this happen in Poland — where the process is now thankfully being reversed — and Hungary, and to some extent the US too.
I’m guessing money is a huge incentive for a lot of these lawyers to make this their industry, particularly when Legal Aid was reduced and a lot of money went out of the industry years ago.
Human rights lawyers earn less than almost any other category of legal professional. Their funding comes mostly from legal aid and charities, or pro bono work in some cases.
I’d love to know how Reform think they are going to handle the massive legal challenges that will exist if they get in and start trying follow Trumps ICE initiatives.
They will change the law to make the legal challenges invalid. Unlike the US, the UK has no written constitution, and with a majority in Parliament you can do pretty much what you like. It's always been assumed that whoever is in power will be "decent chaps".
There is nothing to stop Reform passing a law to make it legal to detain immigrants (including those recently deprived of Indefinite Leave to Remain) in camps, shoot anyone who tries to escape, and gas them in large numbers when it turns out that deporting them is impractical.
Also up for grabs is mass-scale stripping of citizenship from second-generation children of immigrants on the Shamima Begum model. Remember that she had not been convicted of a crime in a UK court. So they could take UK nationality from literally anyone who is still entitled to citizenship of another country via their parents.
One of the first things to go will be all forms of anti-discrimination legislation. It will become legal to shout "Fuck off P*" in the street. And about 10% of the UK population will absolutely love that.