travail can mean the workplace, not just work in the sense of something one does. Per TLFi:

3. P. méton.

a) Lieu où s’exerce cette activité. Synon. atelier, bureau, chantier, usine.Aller, être au travail; sortir du travail.

Hence, you should think of it as the French equivalent of the substitution of “work” for “the office,” “the factory,” etc. (Compare I’m going to work <=> I’m going to the office) Here, work is a location, not an indication of method as is the case in the phrase à pied. (Example for à pied from TLFi: Je remontais à pied les Champs-Élysées.) Consequently, a definite article is necessary, and as the article is le, it is combined with à to form au.

Observe also that this also applies to other expressions that normally would not use a definite article in English. For example:

• Je vais à l’école. I am going to school. (But, word-for-word: I am going to the school.)

• Pourquoi étudier à l’université? Why study at university? (Refers to the pursuit of higher education, not attendance at a particular university.)

In these cases, we are arguably referring to work, school, or university as abstract general concepts. French typically requires articles for nouns unless they are modified by determiners or possessive pronouns, and for general concepts, the definite article is used.

• Mais les femmes sont toutes belles. But women are all beautiful. (Refers to women in general, not a specific group of women.)

• L’amour est un oiseau rebelle. Love is a rebellious bird.

(note that I would have commented directly under the post if StackExchange would let me do it…)

Although Maroon’s answer is correct, Maroon also misunderstood the question. I think the OP did understand that “travail” here was a location, the question is why is it “au” and not “à” for certain locations. Plus, in English “work” is also

a place where someone goes to do their job

as per what Macmillan Dictionary says.

So basically yes, you would need an article (le) in French, and à + le is au. Articles are nearly always required in French.