To begin with, as usually stated, Oxford emphasises GCSEs more than Cambridge, so if your GCSEs are relatively weaker it's usually a better idea to focus on Cambridge. However both consider your grades in context, and if you are eligible for free school lunches this is I believe normally one of the contextual flags they consider, so your GCSE grades may be considered better in that context than you might otherwise believe.
Even beside that, for Oxford it does vary somewhat between courses anyway. Generally if there is a pre-interview admissions assessment, this will often count for a lot - so doing very well in e.g. the PAT may ameliorate weaker GCSE grades. Of course this does vary; while medicine does also take account of the BMAT, GCSEs are still quite important (and for medicine, your GCSEs by themselves are probably not that competitive; I don't know how much the contextual factors may weight that though).
I think in view of the contextual flag, and the fact that you could potentially do extremely well in the ELAT and that may outweight weaker GCSEs anyway (along with the fact that ELL at Oxford interivews a relatively high proportion of applicants anyway) it is certainly a possibility. That said, I might still be inclined to recommend Cambridge as an alternative consideration just to be on the "safe side" as I think it's very likely you would be interviewed and "in the running" from the start provided you are predicted A*AA.
Is there a particular aspect of the course at Oxford that appeals to you more than at Cambridge? Bearing in mind if you're particularly interested in English philology (i.e. Old/Middle English) you can take medieval literature courses at Cambridge and I believe borrow the relevant language papers from the ASNAC tripos. That said, if your interest is particularly in that medieval period, ASNAC would probably be the more appealing course even over the course II ELL at Oxford anyway!