I think believing the first lie that conservatives would really reduce immigration is the product of trusting politicians too much.
Another faction of the pro-Brexiteers would think of the system in terms of a uniparty. The fundamentalists like Farage have no chance of getting elected as PM in the British system, though he did get an MP seat now.
Would things change if Farage were PM? I'm cynical, probably not.
There was a fundamental lie / delusion at the heart of the claim. The second thing a trade deal with another country implies "allow more of our nationals to migrate, and make it easier for them to come over". (The first thing is obviously: "let our products in".)
And this can be seen from the raw numbers too. Before brexit, the annual net migration to UK was about 300k. After brexit, the annual net migration to UK is ~700k.[0] (745k in 2022, 680k in 2023.) And quite a bit of that from the fresh trade partners.
The best way I have heard anyone describe the disaster that's Brexit was as "nostalgic self-immolation for the population who still dream of the Britain where faces were white, passports were blue, and the map was Imperial Pink."
We will be able to negotiate excellent trade deals outside the EU effortlessly
The EU need our trade so badly we will be able to negotiate a seamless trade deal with them
… and many others.