I've already received an offer from the firm that made you one But I'm hoping to get an offer with a firm of equal standing in corp work (you should know which one I'm referring to)

In response to the slightly patronising (?) posts above that I suspect may be by the same individual(s) - just for some context, I'm attending a upper-mid tier uni outside of London with a strong 2:1. I have received rejections from two mid/small sunset firms but I've also received offers from "big/top mid" firms. I also have batch mates with firsts who got their offers even before summer ended.

I recognise the scramble and I recognise that the uni you come from does count. My friends in lower tiered unis are not getting jobs but if you're within the usual batch of top/mid-tiered unis - it's not *that* bad and no you will not end up doing conveyancing in some AMK firm. Don't panic (yet)

Also (1) grades are not end all be all, your cv/CCA/personality counts too. Strong 2:1s and above should at least get you some consideration. (2) interning with a firm would definitely help and if you shine really brightly, it may lead to an offer, who knows. (3) apply early!!
At the end of the day I personally feel that it's a combination of everything - there's no magical formula behind this. But graduating with a first always helps

Just my twocents & speaking out of my own personal experiences with this cycle thus far