Although I agree that you might expect to see some metallic debris on the magnets from the direct clutch hub shaft failing, nevertheless this is a common failure in the 5L40-E and would produce exactly the symptoms that you’ve described. The break can be very clean. Alternatively, it could be an issue (mechanical or hydraulic) with the direct clutch itself. Either way, I think you’ll have to teardown the transmission to fix it.

If you’re handy with a set of spanners and money is tight, I would suggest that you do this yourself and buy a scrap box off eBay for the parts. There’s several on eBay for around the £200 mark. Clearly, you need to check with the seller first that the scrap unit you’re buying didn’t have the same issue (i.e. loss of 4th & 5th gears).

The transmissions are very straightforward to rebuild :
https://xoutpost.com/bmw-sav-forums/...-teardown.html
I can send you 5L40-E workshop manuals etc. if you want to do a bit of research first.

The next cheapest alternative is probably Birch Motors (£1194 incl. fitting).

Phil