Apply for AO jobs as much as you can, because AA is below your qualifications. AO is the right level for people with good A Levels I would say, but the problem is that you may not have experience and to get the 'good roles' you may have to spend 2 years in an 'entry role', unless you apply to the civil service or are careful with applying to places that will take you as an AO. Try phone companies headquarters/local government/local businesses for.
Local council is probably best- I temped in the planning section once and they have a variety of work that isn't all telephone answering. Unless you can get into an admin 'specialism' though, such as arts, finance or environment, then a lot of admin will just be that, and not as challenging as anything you could have got with a degree.
If you do need to start from the bottom then the civil service is a good bet. If you can't get into the AO (or band E1 level) then you can work as an E2 (AA level) for 6 months and then apply for advancement.
Just do research, and if you won't go to uni then it would be good if you did some kind of training to help you, though your ICT is a start- I presume you have Excel and Word knowledge with that that you should stress on your CV.