I would rather say "Днес работих много" or "Много работих днес"

"I worked a lot today" can be translated as 'Я (I) много (a lot) работал (worked) сегодня (today). ' Is съм correct there?' Unfortunately machine translators are not always correct.

Ah, okay, thanks Georgi, that makes sense.

Just to clear it up: "съм" is correct there. It is like "have" in "I've worked a lot today". Actually you can use "Работил съм много"/"Работих много" (and moreover "Забравил съм ключа/Забравих ключа") almost interchangeably. I agree though, simple past tense is far more easier to explain.