The conclusion as reported in the abstract is
One serious flaw in this report is the absence of any substantive definition of a "spiritual understanding of life" available to the people who are being asked whether they have one.
The subjects were participants in the (adult England 2007) National Psychiatric Morbidity Study. That report is available here:
On page 124-125 of the report (physical page 98 of the pdf file), we can see how the information about religion and spirituality were elicited. Not very well.
First there is an affiliation question: "Do you have a specific religion?" and if yes, then. of course, "Which religion is that?"
Then the interviewee is told what the survey means by religion. It appears to relate to the previous question, about a "specific" religion, by enumerating religion-specific names for a place of worship: temple, mosque, church or synagogue, as places where a religious person goes.
"Spiritual" is never defined. Spiritual "beliefs or expereinces" are mentioned as possibly occuring separately from a religion, but not necessarily unavailable from religion, although it seems that an alternative to religion is being presented. Then, armed with this sketchy information regarding what the interviewer is talking about, the respondent is asked about a "religious or spiritual understanding" of their life.
Possible answers are religious, spritual or neither, including combinations of those.
The remaining questions on this point, asked only of those who answer religious or spiritual in their understanding of life, are to rate how "strongly" they hold their "view," on a scale from 0 to 10; the importance of the "practice" of the "belief" also on a 0 - 10 scale, and finally, how often the person attends services or prayer meetings, from never through at least once a week.
The examples in the second follow-up question of "practice" are private meditation and religious services.
Wait a minute. This is incoherent. Religion was distinguished from spirituality on the basis of "actual practice" exemplified by physically visiting any common place of worship. Now, it turns out that "practice" includes both religious services and also private meditation.
Example I, eight bits, practice private meditation. I almost never visit places of worship, especially not for services. Because I "practice," but not (apparently) actually practice, I am "spiritual" but not "religious." Or am I? I wasn't asked about practice, even though that was as much as a definition as I got, rather I was asked about my understanding of my life. Well, I understand my "life" to be my current coporeal presence in time and space - not religious and not spiritual but physical. And may it remain so for a good long time yet to come.
So, I am spiritual, based on my beliefs and experiences, and maybe non-specifically religious depending on how much regular meditation counts as practice after all, but I am neither according to the question that is actually asked.
In the same way that we wonder whether IQ measures intelligence or just skill at taking IQ tests, this questionnaire seems to test not for religion or spirituality, but rather for ESP, reading the survey designer's mind. I am unsurpised that people who are "spiritual but not religious" are more likely to have mental health issues - just figuring out whether that is the correct category is enough to drive someone crazy.