s it advisable to get a mattress topper for a soft mattress

Hi,
My partner and I have just moved into a rented accommodation and he has found that sleeping on the bed in the flat gives him backache due to the lack of support from the mattress. I think it is because it is very soft and gives very little back support. As it isn't our home and quite frankly we are a bit low on space, we do not want to buy another mattress, but someone suggested that we get a mattress topper. Everything I have read on the internet suggests mattress toppers are for added comfort, usually for beds that are too hard. Is it advisable and do you even offer mattress toppers that would help to "harden" an existing mattress and provide more back support? If yes, what am I looking for exactly? Someone suggested memory foam, but I am not sure....is it about the thickness, or something else even?
Thank you for your help and advise in advance.