I'd be surprised, I think most strong philosophy programs require your first degree to be primarily in philosophy - I think occasional exceptions are made for e.g. classics or similar language based grads who are doing philosophy requiring the language(s) they studied and therefore the non-philosophy background is a specific benefit (and they may have encountered philosophy in their first degree anyway).
If your goal is to pursue a PhD and then academic career in philosophy it would probably be sensible to pursue a degree in philosophy, rather than English literature. However I gather the Stirling-St Andrews program has an apparently good conversion course though for non-philosophy grads? I believe there are a couple of other PGDip or masters programmes that enable one to "convert" to philosophy from a non-philosophy undergrad.
I suspect the reverse would also be true - you probably wouldn't be able to pursue a PhD then academic career in English literature (except possibly in literary/critical theory which is a very narrow area) with a background in philosophy rather than literature. There may again be opportunities to "convert" by way of a masters, although depending on the particular area you want to go into this may be a more challenging route.
Don't assume having a background in one humanities field necessarily qualifies you in another! While many humanities fields share similar forms of assessment and may be similarly text based, the actual content of the texts and more importantly, the methodologies and analytical tools they use in approaching them are going to be very different in many cases.
That said as I understand it's in principle possible to change courses once at Cambridge by way of doing Part I in one tripos then Part II in another (the tripos system is sort of designed for that), although in practice this would be subject to suitable academic progress and approval from the directors of study in both subjects.