Imporving accuracy with a No4 Mk1

[Rumpelhardt]

As far as I know smle no.1 front sight blades will not fit. I believe the dovetail is different. I could well be wrong. If so I' sure some one will come along and correct me. There are also two different types of sight blades for the no.4. If the sight mounting block has a screw in the front to tighten the dovetail you need the blades with the solid dovetail. If no screw you need the ones with the split dovetail.
Split dovetail type Lee Enfield SMLE No.4 / 5 Sight Blades Set x8 UNISSUED | eBay
I could not find any solid type but there are usually some listed.
From what I have read side to side movement at the muzzle of the barrel is normal and even desirable as long as it readily springs back to center by itself when moved.