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Not knowing which peep sight you are talking about and assuming your rifle has the original rear sight for a Mk. II as well as assuming that you might not be familiar with the rear sight on a Mk. II, can I state the obvious?
The Mk. II has two peep sights on it. The battle sight is large and it used when the adjustable sight is laying flat. However, if you flip the rear sight ladder up, there is the second peep sight which is much smaller. This is the sight that was used for much more precise targeting.
The two peep sights can be seen in this picture of an Enfield rear sight. If you already knew that and are talking about the smaller of the two rear peep sights then my apologies.
View attachment 87219
Other than that, what Martin said.
I found trying to group at just a 100yds with my No4 Mk1 frustrating. Even the smaller flip peep was large. I did some research about narrowing the peep sight but sold rifle to fund another purchase, also 303 was in short supply at the time.
Here's my research, hope it helps
http://www.milsurps.com/showthread.php?t=14988
related and/or interesting
http://surplusrifle.com/no4/index.asp
http://www.jouster.com/forums/showthread.php?2582-No4-Mk1-shoots-to-the-left
http://www.milsurps.com/content.php...les-3-(Zeroing-of-No.1-No.3-No.4-No.5-Rifles)
http://www.ds-solutions.co.uk/product_info.php?products_id=45
https://www.apexgunparts.com/product_info.php/cPath/30_127/products_id/2610
http://www.arrse.co.uk/shooting-hunting-fishing/109696-enfield-foresight-adjustment.html