For what you want to do it could work out as cheap, and certainly more robust, to buy some 1/2" impact driver bits. I've got a few adapters of various sizes some from Toolstation, Screwfix and some as part of Teng socket sets. All suffer from lash to some extent making it difficult to get the bits accurately in position. The 1/2" set of bits that I bought (i.e. 1/2" sockets with a bit permanently mounted covering a range of Philips, Pozidrove, Square drive, Torx and security screws) are much sounder in use, particularly if using with a pneumatic driver or impact wrench.
Actually at the moment I'm cursing having left all of the air tools in Italy. I've had to rebuild the front end steering knuckles/brakes/bearings on a truck by hand. Some of the screws and bolts were difficult to get at but a piece of cake using air tools.
This set includes the adapter you're after:
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the adapter, which costs almost as much:
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it isn't available.
Or there's this:
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which you will also need 1/2" -> 3/8" and 3/8" -> 1/4" adapters.
If it's that sloppy, cut some shims from a tin can (or try metric/BS etc sockets until you get a tighter one.).. Blue tack holds the bits in. I've done it this way for years and have also made a long extension to use 1/4" driven sockets, by sawing off the angled end of an Allen key and squaring off one end. I've been using this method with my old 1/2" impact driver - the kind you actually hammer - for many years. At a pinch you can also get a spanner on the square end for extra leverage.
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