Trying to find a vicar/priest/minister/etc in a church might actually prove to be a practical problem. Many churches are often served by a vicar (etc) who conducts services across several different parishes. He (or she) might only be present within a particular church building on, say, the third Sunday in each month.
However if you can find a vicar etc) he/she will undoubtedly try to find the time to speak to you but vicars live in the same world as everyone else and they might, for example, have to rush off to collect their kids from playgroup.
Even so, you might find it worthwhile to talk to a 'man of God', simply because you'll know that you'll be speaking in confidence to a stranger (which can often be easier than speaking to a friend or relative). I'm strongly 'anti-religion' but my occasional contacts with vicars (etc) have never left me feeling in any way pressurised to attend church services, or to otherwise get involved with organised religion.
If you feel that it's what you want to do, go for it (remembering, of course, that you might actually find it quite hard to locate a priest or vicar within a church). I'm sure that the person you speak to won't feel offended if you end up saying "I'm sorry. This isn't for me after all. I've got to go".
Chris