One often hears or reads that intuitionism was inter alia geared to avoid Cantor's uncountable sets, and it may be that this was Brouwer's plan. But are there accounts which demonstrate that early intuitionism (i.e. before the advent of modern intuitionistic set theories, which either do not have the power set or do accept Cantor's conclusion) had some intuitionistically reasonable way of evading Cantor's uncountable sets?

I have the distinct memory of having often heard and read that intuitionism was inter alia geared to avoid Cantor's uncountable sets, and it may be that this was Brouwer's plan. But are there accounts which demonstrate that early intuitionism (i.e. before the advent of modern intuitionistic set theories, which either do not have the power set or do accept Cantor's conclusion) had some intuitionistically reasonable way of evading Cantor's uncountable sets?