Becoming an Accountant in the UK help ?

Basically I am coming to the end of my degree this summer and hoping to achieve a 2.1 classification in accounting and finance , along with this degree i also get ACCA exemption from all 9 foundation papers , my problem is that I have no accounting experience which I am really keen to get , I contacted AAT which is the accounting technician qualification which is basically entry level accounting , they said as my degree covers all topics they will award me full membership Level 4 once i work in a firm for a month or so , but my problem is usually people get into a firm whilst studying AAT then if they are capable enough go on to study ACCA/ACA , so I have kinda done it backwards , I really just want to get my foot through the door but it is against the law for me to do some form of AAT apprentiship as I am over qualified ( they wont pay me to learn something i already know ) , so will accountancy firms just let me go in with ACCA F1-F9 exempt ? Any advice would be great :)