(This may have been put in place some time ago, but it's not something we've already covered, so....)
According to the BBC iPlayer support page:
The BBC has retired the BBC iPlayer full programme downloads service on the following phones:
Nokia 5800, E71, N8, N85, N86, N96, N97
Samsung CorbyPro/ Genio Slide (GT-B5310)
Samsung Monte (GT-S5620)
Samsung Omnia II (i8000)
Samsung Pixon (M8800)
Samsung Wave (GT-S8500)
Sony Ericsson Aino U10i
Sony Ericsson Satio U1i
Sony Ericsson W995
The BBC regularly reviews its services to ensure we deliver maximum value for licence fee payers.
Over the last year, we have seen demand for full programme downloads decrease by over 87% on these phones. We have therefore decided that it is no longer cost effective to maintain the downloads service for an ever decreasing number of people.
We appreciate that this will be an inconvenience for those people who have been using the downloads service and hope that you understand why we have decided to discontinue the service.
The BBC will continue to offer users of these devices the ability to stream programmes.
This last sentence is good to know, so users of older Symbian phones won't be left totally out in the cold.
I'd noticed some time ago that iPlayer-sourced MP4 downloads failed to play properly on older devices like the Nokia X6 and 5800, so this is just official confirmation.
Full programme downloads continue to work on the Symbian^3 range (N8, E7, etc.), even under Nokia Belle OS. Of note is that the BBC still hasn't got round to adding the Nokia 701 and 808 to its licensed device database (to enable DRM downloads) - I've emailed them and am awaiting a response.