Hi,
Even "across the pond" you can view some records at your nearest LDS family History Centre. If you go to
www.familysearch.org and click on the "Library" tag at the top, underneath will be "Family History Centres". If you click on this you should be able to find if there is a centre located near you. If there is go to "Family History Library Centre" Type Sheffield in the place box and England in the "part of" box. From there go to Sheffield (second option down). It should then bring up a list of all films that the LDS have. I think St. Peters will be the Parish Church of Sheffield and not actually named.
So for instance, scroll down to Bishops Transcripts for 1608 - 1828 Church of England Parish Church of Sheffield and click it. In the top right hand corner you will see "View Film Notes". Click on this and it will give you the film numbers that you can order from your nearest LDS Centre. They charge a small fee for each film and it is kept there for you to view for approximately three weeks .
Regards,
Mo