The problem is, and I have this with my tenants, that older houses were not built to have dpcs and as LBTR says, in the old days people actually ventilated their houses.
My tenants don't heat the house, don't open the windows very often and mank at times that there is mould. If they moved their furniture away from the radiators so the air could move, opened the windows and had the heating on, then there wouldn't be a problem. When I go back once a year, I just get some chemical mould remover; treat the spots they are moaning about, repeat the advice about heating and ventilation and repeat the process the next year. The dpc isn't the problem here for the OP methinks, but stalled air, and not enough ventilation.
If it were me, and what I have done in two of my former homes, which were old as well, is to ventilate, use anti damp paint, and hey presto, the problem goes away.
When we get posted home and my tenants have gone, I will move back in and kick the heating on solidly for six months, open windows and it will sort itself. After all, the house has been there since 1835 without a dpc!
There is no guarantee at all on an older property that a modern dpc will work. There are other fixes that can be done first, including ensuring that there is no crap under the floorboards so that air can circulate freely in and out of the air bricks.