Thank you guys for your replies!
council tax bills, paid utility bills - they are included in the rent.
jsa, income support letters, housing association letters, child benefit letters - I have not claimed any benefits.
HMRC tax letters - the last one is from April.
rent payments - good idea, I will send bank statements, hoping they will recognise them as proof, because as far as I can remember, when applying for naturalisation online, I have seen somewhere that (only?) bank statements cannot be used as proof of living here.
Thank you for the suggestion.