I opened a HSBC account in UK(based on HK's bank balance) and my son opened his own (arranged by school). No minimum requirement for both accounts. Through HSBC's global transfer, I transfer money to my UK account and then transfer from my UK account to son's account. Free of charge for both transactions. The UK account also provide the credit card, debit card and cheque book, therefore I can pay the school fee by cheque.
Do NOT pay for a bank account. The banks in UK did not start charging international students until recently. You can get an account for free from other banks like NxXWest. Sometimes you get more benefits such as a free railcard, good phone deals. HXBC is misleading people on opening bank accounts that carry a charge. A normal child account has higher interest. In fact, many parents in UK make good use of their child bank account to save money for tax reason. The child account does not have to pay tax (tax is payable in UK for interest).