Water backing up in shower

Hi, I live in the ground floor flat of a three story block (including ground floor) built in the 1950s . I have had a recurrent problem that has manifested itself again and am now looking for a more permanent solution. I have a toilet/ bathroom that has a sink and shower and also a sink in the kitchen. I take care, am meticulous in fact in stopping waste, grease and other potential causes of blockages from going down the sinks and am at a loss as to why this keeps happening. Despite these measures I am finding water backing up through the shower if I use either the sink in the bathroom and or kitchen. The faster the flow of water or quantity the more of a problem this causes and the shower drain gurgles as the water backs up. This has gotten progressively worse over the last couple of weeks and now the water from the sink does not to be flowing particularly fast for this to occur. Previously the backflow would drain back down the shower drain relatively quickly but now takes much longer. There is also a backflow into the shower if I use the washing machine which is located in the kitchen. At the moment the sinks in both kitchen and bathroom seem to drain fairly quickly and I suspect that the blockage may be located in the main stack. I further suspect that given the age of the flats that rather than seperate pipes feeding into the main stack that all the pipes feed into some sort of junction at the stack thus making it more likely to be blocked at that point. This has occurred twice before and on both occasions I had to have dyno-rod come out to unblock. On one occasion water no longer drained out of the kitchen and bathroom sinks at all. The chap who came out used his electrical snake down through both sinks and the shower drain to clear the blockage. After having this done there is a period of approximately 2 1/2 to 3 years before the problem gradually worsens. As I mentioned above I suspect that this is caused more by a case of a bad plumbing system than anything else. I have tried to locate building plans for the bloc through the council (who wee responsible for building them) but with no joy. Any advice as to the cause and what possible (more permanent) solution there is to this problem and potential costs involved would be most gratefully received. Many thanks for taking the time to read and respond to this query.