Most agents use referencing agencies. You'll be expected to earn 3 times the rent to pass. If you don't earn enough, they'll ask for a guarantor.
If you don't earn enough and say that you're planning to apply for housing benefit or whatever, then most landlords will say no. Estate agents aren't supposed to say they won't take DSS, they can say they don't have any landlords who won't accept DSS.
If the tenant is on housing benefit, it's very hard for them to move. If you're looking to move, then you'd need 6 weeks security deposit, and months rent in advance. The council won't provide you with this, and if you have that much in savings I'm pretty sure they won't be giving you any benefit to begin with. Housing benefit payments are strange, they tend to pay weekly or some variation, whereas most ASTs are based on calendar months, so for a lot of the time, a DSS tenant would technically be in arrears. This voids a lot of landlord rental insurance.
If your landlord has served notice on you, then the council won't rehouse you until you can present them with an eviction notice. So there are lots of fun and games involving courts.