Whether or not you can take History A-Level without the GCSE is up to the discretion of the school. It is not usually a prerequisite but it is recommended. Other than English and Maths, generally speaking, there are no specific GCSE subjects required as it will be your A-Level subjects.
For Oxford PPE, Maths is recommended. Since you are coming from what I assume is a large independent boarding school, you can treat this recommendation as a quasi-requirement. They state that History may be of useful preparation so it may be worth looking into it more if it's the topics in the GCSE specification you dislike and not the subject area as a whole. Politics, Economics and Philosophy A-Levels may also help, and, since Maths is recommended, Further Maths may also be useful.
For Cambridge Economics, Maths is required. The course overall is very Maths-heavy - I'd say they do more Statistics than us Maths students, particularly in the earlier years - so Further Maths is very useful, with 93% of successful applicants having it. Similarly, Economics A-Level is also taken by 93%, with 86% taking both Economics and Further Maths. If you're coming from a particularly well-performing school, especially an independent school, then they may be less lenient with your not having them, as many of the students who don't have them won't have had them as options at their schools.
Overall, your GCSE subject choices really shouldn't make much difference, provided that they permit you to do the necessary A-Levels.
I should mention that Oxford PPE and Cambridge Economics are really quite different courses. Oxford also has Economics and Management which is more similar to Cambridge Economics. Furthermore, if you are still at the stage of choosing your GCSEs, you are really looking ahead too early, especially for choosing courses that you likely won't have studied at school.