Blockchain.info replied and said they cannot help in terms of resetting a password.
I am totally lost here

Yes blockchain.info doesn't store your password so they don't allow resetting password. Have you tried like when verification link is sended to your email keep open than tab and open your email. Click the link that will be open in next tab. And when you again go back and check first tab that is opened you should logged into your dashboard. As you only get link after you enter password for the wallet but don't know they send link even password is wrong or not.
I have tried that already and it does not work. With the two tabs open, the 'first' tab should get you into the dashboard, but it keeps saying: "Please check that your password is correct".
It seems I lost my precious BTC

If you really haven't store your seed A.K.A the 12 words and you keep getting incorrect password than there is nothing blockchain support as they really don't store the password. You should always keep the seed in some protected document in your computer as with it you can restore your wallet from any other PC. I am afraid that I have to say that this time is not the blockchain fault but the user fault for not saving the most important thing in a bitcoin wallet which is the SEED.