Slow draining downstairs toilet with backflow from upstairs toilet

I'm from England and have recently moved into a new house and am experiencing some issues with the downstairs toilet. When you use the upstairs toilet a tiny amount of dirty water comes back up through the downstairs toilet. The water in the downstairs toilet goes down by around a cm and then back up and this repeats once or twice. The backflow is most noticeable when you flush the toilet upstairs whilst the shower is on. To me it seems like a partial blockage so I have tried plunging it and a drain coil but nothing seems to have worked. To make things more annoying I don't think our property has got a drain inspection point and I suspect it is somewhere on our adjoining neighbour's land but we've spoken to them and they don't know where it would be.