I had a similar problem once, I know how it affects your whole life, and if you can't relax at home its awful.
I moved into a house I had bought to find I had neighbours who installed a tumble dryer in the cupboard under the stairs where the party wall is. Sounds like nothing doesnt it? But the thing was on every night from midnight til 4am (economy 7?) and every 90 seconds would change tumble direction. Every night lying awake waiting for the next 'boooom' as the direction changed. Earplugs, as you say, were useless.
After a few weeks of sleepless nights I had a calm word. They seemed a reasonable nice family until then.
From that point on I had loud music played continuously, the tumble dryer of course still on and abuse in the street/doorstep. When they noticed I would go in the garden when the music got too much, they put a stereo out there too.
3 months after I moved in, I moved out, back into a flatshare, and put the place up for sale.
I sold the house for 15K less than I paid for it, plus all the selling costs. It took another four years of flatshare to save up enough to buy somewhere again.
I have never regretted it. Best thing I ever did for my own sanity. And now I really understand the value of good neighbours!
I hope your situation gets resolved.