Rented basement flat - how to get rid of musty smell?

I am trying to explore every avenue!

We live in a basement flat of an old victorian building. We love the flat and when we first moved in, I couldn't detect any musty smells although the previous tenant said that sometimes, if you are out for a few days it can be a bit musty. There is no visible damp in the flat but the flooring is all carpet.

We moved into the property in Autumn and as the heating is included in the rent, the rooms were generally quite dry so we couldn't smell anything (heating is running between October and April). Over the summer there is no heating at all which is not a problem but as we don't have very warm summers (and this year was rather wet anyway), we realized that the hallway and the bedroom started smelling quite musty. There is no mold on the walls but there can be a bit of condensation on the bedroom windows in the morning if I am drying my clothes (not that much). The only rooms that don't smell at all are the living room, the bathroom and the kitchen. All rooms in the flat are very large so it can be difficult to cover the smell. The only opening in the hallway is the entrance door. The bathroom has an extractor fan - as it has no window - which is being switched on automatically when you turn on the lights. Then there is the bedroom which has windows but is quite dark (so is the hallway). Both rooms smell very musty. There is a built in vent in the bedroom-wall and the landlord provided a small dehumidifier for the bedroom (which I don't think is enough).

As it keeps raining I can't dry my clothing outside which contributes to the problem. I noticed that some suitcases that I stored in the bedroom caught some mold but I was able to wipe that off with antibacterial wipes and it didn't come back. However, the smell is always hanging in the air. I can't wipe the floors as they are all carpet and there is not much I can clean with bleach. I tried sprays and candles but I would have to keep using them as the solution is only temporary. Baking soda and all that stuff only helps in smaller rooms. As both rooms are very big I need a solution that keeps the smell away permanently and on a larger area. I know some will point out health hazards but I guess that's just the thing with basement flats - there is always a bit of a musty smell around them - Or is there anything that can be done? Do I have any rights at all since the walls are not covered in mold but there is only a bit of a smell?

Can anyone please give me some tips and hints how to cover the smell and/or to prevent the problem of damp all together?

Should I ask my landlord to get laminate and get rid of the carpet?

Would it help to put vinegar in an oil burner? (silly question but maybe it helps??)