Ophelia you need to post this as a reply to your original question, then all those who responded will get an alert to know there is a new comment.

I remember the original question - in the circumstances, Ophelia, I would take the advice of a landscape architect or a highly qualified arboriculturalist - you've not said how large the trees are currently, but sometimes, cutting trees down increases rather than solves the problem. If the trees are old and mature, reducing their water uptake may cause more problems. If the trees haven't been in too long, then it might be worth pollarding them to see if it helps.

Poplar tree roots are as long as the tree is high, if you get my drift, so it will cause probems to buildings if they are growing nearby.

The trees are mature, and are about 70-80 feet in height. Other poplar trees in other neighbours gardens have been pollarded with seemingly no problems.

Ophelia, if you say the trees are 70-80' in height then the roots are bound to be under your conservatory if they are only 50' away! Maybe some soil samples will show what is causing the problem and even some roots may be found in the soil. We have just had this kind of problem sorted out by an offending cherry tree 15' from our front door! It has taken four years (one year to monitor) to get the tree removed and our house re-built!