It sounds as if you might have some interconnections between circuits, so you would have to pull out more than one fuse to remove power from a circuit. If that is the case, then it is dangerous and should be properly investigated straight away.
The chap who owned our house before us clearly believed he had more electrical knowledge than he did...
He decided to fit a second, smaller, consumer unit next to the original wylex board. He fed this using 4mm2 singles eek from the incoming terminals of the original wylex board (protected by the 100A DNO fuse). He then decided that the largest of the 3 ring finals in the house needed to be 'upgraded' so .... one leg of the ring was fed from a 40A () MCB in one consumer unit & returned to a 32A MCB in the second consumer unit! Hey presto a 72A ring final and neither board isolated by turning off just one main switch! Took me a while to sus that one out!