What was Lady Bracknell's objection to Worthing as a husband to Gwendolen?

Mr Worthing was found inside a black handbag by Thomas Cardew in Victoria Station, so, he doesn't have parents and nobody knows about his real family. As a consequence of that, Lady Bracknell thinks that Worthing is not a suitable husband for her polite and only daughter Gwendolen, so she doesn't permit to her daughter to be engaged with Ernest. If Ernest wants to get marry with Miss Fairfax, he must find relatives and produce at least one parent. True?