There is no consensus among critics about whether Wide Sargasso Sea stands on its own or not. For example, Francis Wyndham wrote in his introduction to the first edition (1966):
For many years, Jean Rhys has been haunted by the figure of the first Mrs Rochester—the mad wife in Jane Eyre. The present novel—completed at last after much revision and agonized rejection of earlier versions—is her story. Not, of course, literally so: it is in no sense a pastiche of Charlotte Brontë and exists on its own right, quite independent of Jane Eyre.
In "All That Foolishness / That All Foolishness: Race and Carribean Culture as Thematics of Liberation in Jean Rhys' Wide Sargasso Sea" (Critica 2.2, 1990), Sandra Drake wrote,
The novel stands on its own. It could have been written without the relationship of intertextual referentiality of Jane Eyre.
In addition, Jean Rhys wrote in a letter to Francis Wyndham dated 14 April 1964:
I think there were several Antoinettes and Mr Rochesters. Indeed I am sure. Mine is not Miss Bronẗ́̈́ë's, though much suggested by "Jane Eyre". She is, to start with, young not old. She is still a girl when she fires the house and jumps to her death.
However, neither this statement nor Sandra Drake's deny the deliberate intertextuality between Wide Sargasso Sea and Jane Eyre.
In the New York Times Book Review of 18 June 1967, Walter Allen wrote that Wide Sargasso Sea is only,
a triumph of atmosphere [which] does not exist in its own right, as Mr. Rochester is almost as shadowy as Charlotte Brontë's Bertha Mason."
(It is not clear why Allen claims that "Mr. Rochester is almost as shadowy as Charlotte Brontë's Bertha Mason", since Part Two, which represents more than 60% of the novel, is told from Rochester's point of view.)
Michael Thorpe wrote in 1977:
Though I have seen people ignorant of Jane Eyre respond to this novel as a self-sufficient work, it would be foolish to deny that many average readers come to it with some recollection of Jane Eyre and that Rhys relied in a general way on their doing so.
In "Burning Down the House: The Revisionary Paradigm of Jean Rhys's Wide Sargasso Sea" (1993), Caroline Rody wrote,
Thorpe disagrees with Allen, as does another critic, Arnold A. Davidson, who argues vehemently for the text's wholeness, citing as precedents the famous literary borrowings of Shakespeare, Joyce, and others. (...) In striking contrast to these three male critics, none of the dozen or more female critics I have read finds it necessary to consider the "crucial" question of the autonomy of Rhys's text; most are interested, rather, in the nature of its attachment to Jane Eyre. The suggestively grim and awesome imperative that a text "stand and be judged alone" is alien to the model of inheritance implicit in Wide Sargasso Sea, which privileges relationships — to a mother first and, I shall argue, to daughters to come.
Obviously, all the critics cited above were familiar with Jane Eyre; I doubt that they know what it is like to read Wide Sargasso Sea without being familiar with Charlotte Brontë's novel. On a superficial level, the first two parts of Rhys' novel can easily be read without any knowledge of Jane Eyre; it's only at the beginning of Part Three (the shortest part) that "Grace Poole", "Leah" and "Mrs Eff" may confuse readers who are unfamiliar with Jane Eyre. However, readers should be aware that the intertextuality between the two texts goes deeper than the level of the plot and the characters' names. Readers who are not familiar with Jane Eyre will not understand in what way "rewrites" the story of Bertha Mason/Antoinette Cosway and Edward Rochester.