The singer labelled Lydia and her mother Debbie as desperate for fame after they posted a picture of themselves posing with a magazine that they had featured in on the microblogging site.
Parker wrote on Twitter: "@LydiaRoseBright @debbietowie how ironic is that picture. Is that what you lot call yourselves these days for doing nothing!! #shocking. (sic)"
Debbie soon wrote back: "@TomTheWanted don't embarrass yourself. something I live by if you've got nothing nice to say don't say anything at all. Haven't you got a life?"
The Only Way is Essex star Mario Falcone then weighed in on the argument, referring to Parker as merely the "backing singer" for The Wanted, joking: "Keep hiding behind [bandmate] Max [George]." He then referred to him as "the ugly one in the band". Parker fired back, calling Falcone a "2nd class Mark Wright".
Debbie later tweeted: "You must realise you start on me you'll be battered by TOWIE family. We should find out as much as possible about someone before coming into conflict with them."
After the online argument, Lydia wrote on her Twitter page: "Quite upset to look on twitter & c @TomTheWanted putting me & my mum down. Sad to see people constantly being bitter is there really any need. Sad that in the world u will always find anger & bitterness. Thankfully there is also love & laughter. Don't ever let people put you down x."
> 'TOWIE': Debbie Bright warns Arg off Lydia, tells him to 'man up'
> The Wanted's Tom Parker: "I think I'll get married soon"