There are a couple of issues with respect to making up a .22RF Lee Enfield. There are C No. 7 receivers available. They look new, but if you examine one carefully, you will see that these have been refinished, before being placed in stores as spares. It is my understanding that the ones floating around are from a batch of about 400. These receivers are not expensive. Of course, a No. 4 receiver can be used. This simulates a No. 9 rifle.
An available .22 barrel can be fitted into a breechpiece made from either a .303 barrel or a piece of barstock. The trick is to find a long enough .22 barrel. Because of the stocking, it is not apparent that such a barrel has been used. Take a No. 4 front sight base, sleeve it with a bushing and fit this to the replacement barrel.
If you look at the breeching of a .303, you will notice that there is a gap between the breechface of the barrel and the boltface. This is where the rim sits, and the gap is related to headspace. For a .22, an altered .303 barrel has to be brought back to the boltface. You cannot have over 1/16" of .22 case hanging out in the breeze. There are two ways to eliminate this gap. The barrel's shoulder can be machined back one turn, and the breechface altered. If this is done, the forend nosecap and upper handguard cap will have to be set back as well.
Or, when a filler piece for the .303 chamber is machined, it can have a flange incorporated which serves to lengthen the barrel some 1/16". This chamber filler can be soldered or bonded into place. If a 5/16" liner is used, the liner drill is run right through the bore and the chamber insert after the insert is installed. The chamber filling insert can be machined to resemble a .303 case, or the chamber can be opened out and a cylindrical insert installed. Ream the chamber after the breeching is done.
A .303 bolthead can be adapted for rimfire, if a .22 bolthead cannot be located. The firing pin hole is plugged, and an offset two diameter hole machined for the .22 firing pin. A .22 extractor will be need, and can be made if necessary. A .303 firing pin can be easily altered to be used with a floating .22 firing pin.
I've converted No. 4s using both barrel systems, and both work.
If I do another it will be a SMLE, simulating the WWI period training rifles.
No. 5 lookalikes in .22LR have been made, as well.
Years ago I had an unfinished C No. 7 barrel with a bad bore near the muzzle, sold it as is. I know it was used to make a No. 5 pattern rifle in .22RF. Big advantage to making a No. 5ish rifle is that the shorter barrel makes finding a suitable .22 barrel that much easier.