Although I am considering the Beachy Heads because it's a very beautiful place to end it all, if I had to pick another spot my top choice would be the Bristol Suspension Bridge. Most trains and coaches moving from London to the South West pass through Bristol so it's logistically easier and cheaper to arrange to get there in my opinion, depending on wherever you live. Although in recent times I have heard that the local authorities have put safety nets below the bridge, it still seems to be a nice place to ctb. The bridge is built between two cliffs overlooking Bristol and the drop below is just huge, with impact on water.
Here is a picture from google:
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However, jumping into water (even from a bridge this high) will come with a little chance of survival, in which case it would be very painful and agonising. Are you sure that you really want to go ahead with it? I'm still around if you want to talk through things going on in your life that are affecting you and if you want my help. Other than that, I wish that you find peace in whatever you choose to do.