I don't know of any differences between the UK and USA with the grammar of phrasal verbs. Phil's explanation is applicable in the UK too. In both countries, "work out" is the verb and "workout" is the noun.

Phrasal verbs always have at least two words, separated by a space e.g. get through, put off.  

Nouns which come from phrasal verbs are either one word e.g. workout, or two words connected with a hyphen e.g. turn-off.  But they are never in the same form as the verb.  It is hard to guess if there is a hyphen or not, and I don't know of any strict rule.  

Phrasal verbs with "out" often have one word nouns e.g. knockout, fallout, turnout.  But then with "up" there is "stitch-up" and "startup".  If you are interested, there are some other patterns with other prepositions.

Phrasal verbs always take a space in English (the particle is stressed in speech), unlike German. The noun forms are often written as one word -- the particle loses the primary stress.

He worked out at the gym.

He had a good workout.

I agree with Michael that whether or not to hyphenate these nouns is really hard to predict. Actually, hyphenating nouns is generally an area where there is a lack of agreement among native speakers. It’s really more a matter of style than grammar or even spelling. Regardless of which country people are from, there seems to be a lot of regional, idiosyncratic, and even generational variation. For example “on-line” or “online” — which is it? :)

My advice is that there are a lot more pressing issues for the ESL learner to pay attention to. For example, the proper spelling of “character.” A simple solution would be to double check your work by running a quick spell check. (When in doubt, write the noun with no hyphen, and the spellcheck will pick it up… not that spell-check is a perfect solution… heh, heh, heh.)