Richard said, "I learnt to dance at school."

Do Brits generally use the forms learnt, spelt, etc., rather than learned, spelled, etc.?

What's the genesis of those forms?

1. Yes.

2. No idea

I'd say that they are modern spellings of words that show that the suffix for the preterite in English is in some environments devoiced. When the e in the suffix was still being pronounced, the d remained voiced, but later when the schwa was dropped, the d became a t.

learnèd > learn'd > learnt.

We don't usually do something like this. Compare the final s in the standard English plural. It isn't respelled in words which end in a voiced consonant to a z.

week ~ weeks
dog ~ *dogz
(and while we're at it) church ~ *churchiz.

Just another example of our arbitrary orthography at work.