The requirement to buy a new KS mattress for a slatted bedstead

I am 49, single, 5'5" tall and weigh 10.5 stone. I suffer with lower back pain due mainly to a sedentary job sitting at a computer. I have a king size Nolte Mobel slatted bedstead with an 8 year old mattress on it which for the past year has been making my back ache worse. This mattress is a Harrison Serenade 1440 springs/" title="pocket spring">pocket spring count, with a mattress spring count of 1060 and a pocket sprung base count of 380. I have been sleeping on a spare double mattress on a divan bed which seems to help - this mattress is a Slumberland Bronze Seal 1100 pocket sprung mattress. My budget is about £600 ish. What would you recommend as the best mattress for me/my budget? I would love to wake up with no back pain at all ...