I am a LL and have tenants on benefits.
I don't have a mortgage so don't have to tell anyone. However, I had to search harder for insurance to find someone who would cover tenants on benefits and I did then have to pay a premium for it.
My tenant has been excellent. He has a guarantor (parent) and has never been late with rent and is very pleasant to deal with.
So, it might be that larger landlords who own a number if properties and might be less likely to have mortgages might have more flexibility. If you don't meet the affordability criteria though, you will need a guarantor and also might expect their bent to be a little higher to cover additional costs such as bigger premium insurance.
I agree it is really tough. However, the mortgage issue plus higher insurance premiums (and you to have to search quite hard to find an insurance company that will take tenenats in benefits) plus the reports of more liklihood of damage do out people off.
Unfortunately, statistically, those on benefits are a greater risk - that is why mortgage companies say no and insurance premiums are higher.
It's the same as always - a few bad eggs tarnish everyone else and all the good tenants lose out. The trouble for landlords is that it isn't always easy to tell who the good or bad tenants are.
I think all you can do is to make sure you have everything you can in your favour - so make sure you will have excellent references at this place, have always paid on time and leave places in a great condition, have a guarantor lined up and unfortunately be prepared to pay a bit more. You will find somewhere, but you will probably have less choice and not get offered the best properties.
I hope you can stay where you are for as long as you'd like.