The results of an NCR statistical survey on core beliefs of Catholics in the USA and their analysis can be read here.
I don't think a similar exercise has been done in the UK but I think that the USA results are likely to be mirrored here (IMHO.)
The article is marred because it does not give the total number of people involved in the survey ( bad !) nor does it give any further demographic details (bad !). The full report is available as paper copy to purchase but not available as a pdf file to download online which is also a pity for those overseas.
Nevertheless there are some interesting results here :
"Most strikingly, only one in five Catholics (21 percent) says that a celibate, male clergy is very important to them as Catholics, and almost half (46 percent) say that it is not important at all. By the same token, close to two-thirds (62 percent) indicate support for women in the role of priests in the church, and 75 percent express support for women as deacons."....... and only 35 % are opposed to same sex marriage."
These findings in particular give me some cause for hope but are also a source of much frustration !!!
However, I also find the figures on the importance of the Mass and sacraments surprisingly lower than I would expect or hope for.