Speculations in Idealism Berkeley is most decidedly not an empiricist. Berkeley appeals to self-evident truths of reason. He takes it to be self-evident - as did Descartes, of course - that thinking requires a thinker. And on this basis he thinks minds exist.
Note, minds are not empirically detectable. Yet Berkeley believes in them. If he was an empiricist, he wouldn't.
Again: he takes it to be manifest to reason that thoughts require thinkers (and that sensations require sensors).
That's at the heart of his case. It's not an empirical truth - one cannot see, touch, hear, smell or taste that thoughts require minds. It is a manifest truth of reason.
And he takes it to be manifest to reason that our sensations must resemble what they're providing us with some awareness of.
And he takes ti to be manifest to reason that sensations can only resemble other sensations. Just as a texture can't be like a sight, or a sound like a texture, so too no sensation can be like something that is not a sensation.
From this it follows that the sensible world our sensations tell us about must itself be composed of the sensations of a mind.
That's his positive case for idealism.
He also has a destructive case: materialism doesn't make any sense. There is no need to posit any material objects. Plus a material object is extended in space by its very nature. But any object that is extended in space will be infinitely divisible. Yet nothing can be infinitely divisible, for that would involve it having infinite parts - which is to posit an actual infinity. There are no actual infinities in reality, thus there are no extended things.
Now the fallacy that Berkeley is often accused of having committed is the fallacy of confusing a vehicle of awareness with an object of awareness. It's a fallacy that many here commit. The fallacy involves going from "I think that p" to "p is therefore a thought". Lots of you commit it when you try and think about morality. You go from "I feel some acts are wrong and feel some acts are right" to "rightness and wrongness are feelings of mine". That's the fallacy.
Berkeley is said to have committed it, for he is thought to have argued that as we know the sensible world by sensation, then the sensible world is a sensation.
Yet clearly that is not something he argued. He drew that conclusion, but not in that way. He did not think the world our sensations give us an awareness of is made of those sensations - the sensations that give us an awareness of it. Our sensations are 'of' the world, but do not compose it (thus at no point does he confuse a vehicle of awareness with its object - our sensations are the vehicles of awareness, and the sensations constitutive of the world are their object). HIs point is that in order for them to be 'of' the world, they would need to resemble it. And it is from that, combined with the claim that sensations can only resemble other sensations, that we get to the conclusion that the world is made of sensations (and thus the sensations of a mind).
Perhaps the argument is unsound, but it's not fallacious.
Oh, and he was Irish, not British. The part of Ireland he was from was not part of Britain.