Cockney Rhyming Slang
Brahms and Liszt rhymes with pissed, drunk, inebriated. To have drunk too much alcohol. Brahms and Liszt is normally used with the verb to be. This phrase is most commonly employed only using the first word Brahms, however it is possible to use the full phrase. So the final construction is "to be Brahms. I think the idea of this saying is that people like to sing when they are drunk. So it is saying that a person is feeling musical i.e. drunk.
For example: He's been Brahms every night this week.
He drinks two pints and he's Brahms.
We arrived at the party and everybody was already Brahms.
Johannes Brahms was a nineteenth century German composer. Franz Liszt was a nineteenth century Hungarian pianist and composer.