UK startup here. We signed up a Barclays business account in about ~2 weeks and they were happy with a £100 deposit just so there was something in the account. Relatively straightforward. Paypal set up and seems to be working OK. Not sure why it all went wrong for you.
Having lived in the UK a few times and having to go through the process of bank accounts and stuff, and a lot of friends who did the same, the problem usually isn't the bank.
Its usually the case manager you get. My first account was with HSBC, I waltzed in filled the forms out. Walked out. My friend I travelled with came with me, got a different case manager ... took over 4 weeks and eventually moved to Ireland before his account was even opened.
The differing service you can get from one bank is amazing. Just take this example from a trip I took a few months ago.
I went to Thailand with 3 mates from the UK, all Llyods customers. One had a friend as his bank manager who OK'ed his for use in Thailand. He had no trouble at all.
Second guy OK'd his but he withdrew 20,000 baht in one transaction and his account was locked as he wasn't told there was a threshold. He had to ring help desk to unlock his account, it was fine after that.
Third guy didn't realise he had to OK the account, every time he used an ATM his account was locked. He would ring help desk every few days to unlock his account. It seemed he could only draw down 10,000 baht a week, if he tried a second transaction a few days later it would lock again.
No matter what he asked for they just unlocked his account and promised it would lock again. But we where there for a month, and he was always on the phone to the bank.
The problem they had was with a merchant account, not a business bank account, the two are different and a business account is as easy as setting up a personal account.