I do Hist/Pol at Warwick, you're in luck.
The tutors aren't idiots. They'll know you're applying for straight history. The thing is, the two subjects cover such similar ground (especially for modern history) that you can work around it fairly easily. Do you study both history and politics at A level? In that case it's best to talk about each subject you studied and what you learnt from it, without being too explicit (so don't write 'studying politics helps me look at history in this way' etc). Hist/Pol at Warwick is administered by the History department so I think you'll have to go through them primarily. Though I'm not sure if the politics department checks Hist/Pol statements or whether they just give History a quota to let in.
I'm only going into second year, but I know that module choices are always gonna be fairly restricted due to joint honours. I wasn't able to study French last year as I would have done if I were studying straight history, and this year I have to do political ******* theory which makes me want to shoot myself. That's just something you have to accept with a joint degree. You've also got to expect the departments not to talk to eachother, which in practical terms means that your personal tutor will be History OR Politics and not both. The deadlines sometimes clash but if you're lucky your tutor will teach Hist/Pol seminars and so will set the deadlines accordingly.
P.S. In your personal statement, do not use the quote 'history is past politics, and politics is modern history'. Every Hist/Pol applicant writes that.
Otherwise good luck, is Warwick your first choice?