Your daughter should definitely get a UK bank account once she comes over here. The UK has moved to chip and pin cards, and while it is still possible to use a card with only a magnetic stripe 95% of the time, it's best for your daughter to avoid any surprises and just get a local debit card. Also she will be able to have a UK cheque book which is a necessity.

UK banks can be a pain about opening new accounts but she should be OK as long as she can provide some proof of name (ie passport) and address (bills, bank statements, etc. sent to her UK address and to her previous address in the US). Some may accept a letter from her college with her address on it as well, others may be less accommodating. I personally find the Co-operative Bank to be pretty good with these matters but that is just my own opinion. Best to just walk into the Oxford branch of any of the major banks and ask.