No, banks in the UK do not open accounts for IBCs or other typical offshore companies. They hardly let any foreign company accounts, even from more reputable jurisdictions.
You will most likely need a UK company, if even then as a non-resident. At best you can get a UK bank account with a European company, but that's far from a guarantee.
That could work, yes, but before you waste time and money on setting up the company, contact a couple of banks and see if you can get pre-approval for your business plan.
UK banks care a lot. Unless you bring serious capital to them, they almost always shy away from offshore structures.
You are right in that it's better to be concise. Be honest and upfront, but there is no need to overwhelm them with information. It's better to let them ask the questions.
I've seen offshore companies successfully set up payment processing companies in the UK and get bank accounts there, but that requires an FSA license. Might be something to consider though, depending on the size of your operation.