my brother lee is 38 and autistic. He has put on a lot of weight

Hi Vanessa, Not something I have any experience in sourcing. My first thoughts were to search using the term "bariatric" but I was only able to find links from the US:
http://www.treadmilltalk.com/woodway-bariatric-tread-ergometer.html

http://www.irvinghealthcare.org/index.php?option=com_content&view=article&id=75&Itemid=109

This UK website seems to suggest that the more expensive treadmills are suitable for users up to 20stone
http://www.fitness-superstore.co.uk/treadmills/10026_0c.html

I think your suggestion of emailing the current providers / fitness organisations for advice is a good one and you could include suppliers of physiotherapy equipment in your search (eg http://www.physio-med.com/).
This is obviously a very expensive investment for the person and therefore I would want to be absolutely sure that the person will be able to use it (many of the people I work with really struggle with the concept of the treadmill and can't get into the rhythm required). The dietitian involved with the person may be able to arrange a trial and if successful they may be able to arrange regular access to appropriate equipment.
I'm not sure what weight limit the equipment in "private gyms" is but this may be another option - some gyms will open early / late to allow individuals quiet private sessions.
I wonder what private gyms do with the equipment that they upgrade? Might be worth emailing to ask?
My other suggestion is trusty ebay - if you can find the funding / transport/ volunteers to pick it up http://www.ebay.co.uk/itm/TECHNOGYM-EXCITE-RUN-700-COMMERCIAL-TREADMILL-RUNNING-MACHINE-/300855020324?pt=UK_SportsLeisure_ExerciseFitness_Treadmills_JN&hash=item460c5b4b24 this one has a user weight limit of 28stone!
Let us know how you get on. Arlene