As far as i know all the rentals on the likes of rightmove are private rentals, housing association or council property's aren't advertised in the same way!

If you are looking for a direct rental though from what i have seen the majority of landlords who rent direct tend to either only usually rent to friends or friends of friends, or they tend to rent direct to avoid costs which in some (not all) cases are a sign of a landlord who will shirk their responsibilities towards their tenant! As i said its not always the case, but best to be aware!

Letting agents are a pain in the neck and often don't do a very good job, but they do offer you as a tenant a certain level of protection!

Unfortunately i don't know of any property's available to rent direct (i know a few people with rental property's but they will only deal through letting agents).

Good look in your hunt though!