I am unaware of anyone offering this conversion.
I have converted No. 4 rifles, and am currently in the finishing stages of completing a SMLE .22 assembled primarily from salvaged parts.
Converting a respectable SMLE would not be appropriate. One with a poor bore, mismatched numbers, maybe. Fine SMLEs now command serious prices.
Converting a Lee Enfield involves: machining and installing an insert to fill the .303 chamber, and bring the barrel's breech face back to the bolt face. Drilling the barrel end-to-end, obtaining and installing a liner, chambering it, making an extractor cut, and crowning. Conversion of a .303 bolt head to rimfire, and installation of a .22 extractor, if an original bolt head assembly cannot be found. A C No. 7 extractor will fit a SMLE bolt head. I can't imagine doing the barrel work without removing the barrel from the receiver. That is another complication. Instead of lining a .303 barrel, a replacement barrel could be installed.
Converting a rifle takes time and some skill. If a reasonable hourly rate is charged, the cost will not be insignificant.
This is the sort of job that might make sense as a personal project, but might not be cost effective if a gunsmith must be paid.
How would the cost of acquiring a rifle and having it converted compare with buying a No. 2 Mk. IV rifle?