Without meaning to be rude, its highly unlikely you will get a mortgage on your earnings? Depending on where you are in the country I'd guess your salary needs to be significantly higher.
With regards to the council you need to check with them how easy it would be to get a council/housing association home. I know from experience that in Wokingham its highly unlikely unless you are placed in emergency b&b accommodation and found to be faultless, i.e. no rent or council tax arrears that they would ever be able to provide any housing. However a friend who lives in the Newcastle area, sold a house that they could no longer afford and were able to let a lovely 3 bedroom council house which they moved into after completion of the sale of the house. So it really depends on the housing stock available near you.
If you haven't moved into your private let yet now is the time to negotiate and get things fixed. Its inevitable that things will go wrong and you discover them whilst you live there, but if you have a decent landlord they will ensure that things are fixed in a timely order. I rent and my landlady has British gas cover which covers electrics so anything goes wrong and I can just give BG a call and they come out and deal directly unless its a fault not covered and needs paying for, then they ring the landlady to agree costs and send her the invoice.
Renting isn't all bad, I live in a high cost area, I've lived here for a long time and when I was married owned our own home, now divorced with 4dc even working full time in a well paid job, I can not afford a mortgage for the size of place that I would need, so saving my divorce settlement and anything extra to put away to hopefully buy a small 2 bed place once the dc have left home, assuming that I will still be earning the same amount.
Renting can have advantages especially on a low income as it means essential household repairs are paid for by someone else. If I had brought a house and my boiler needed replacing its unlikely I would have the £1000 plus needed to replace it. So I'd say above all else a good landlord is essential, research your landlord, ask questions such as do they have boiler/gas/electric cover, why did the last people move out, time scales for repairs etc. Remember a good tenant and landlord relationship is essential, if you show that you are treating the property as home and take care, keep it clean and decorated, in return they will show you the respect you deserve, treat the property like a dump, never clean, trash the garden etc. they rightly will get cross and perhaps not be so helpful and want you to leave.