I'm currently a 2nd year Computer Science student (specifically software engineering modules) and, just for context, I've received 83% on average from my 2nd year.
I got BCB in Maths, Chemistry and Biology at A-level, and I only go to a ~40th place university (for Comp Sci). Although it is BCS accredited- which is the main part to look out for- as well as the University receiving a 'silver medal' for TEF. I had the same concerns as you but luckily, comp sci tends to be very different when it comes to employability compared to any other degree sector (as you've seen in the other replies already).
The big tech companies (FANG) like Google, Facebook, Amazon, etc... really don't care what university you went to- and I'm being deadly serious when I say that. In-fact, they frequently employ software engineers who don't even have a degree. But, the key part is, you have to pass the 'dreaded' interview process. It's extremely tough, but it can be easily prepared for and you'll get a massive reward (I'm talking £80k salary + £40k stock + £15k relocation bonus, and the stock amount usually doubles each year you're at the company).
In a way, it's great because it prevents comp sci graduates from lower univerisities being locked out of the top, highest paying jobs- unlike Law, Medicine, Chemical Eng. , Maths/ Statistics for financial positions (quants), etc...
The only resources you need are: Cracking the Coding Interview book by Gayle Laakmann McDowell (well worth the £20) and then, once you've mastered all the Data structures/ algorithms and Big O complexity, just use LeetCode.com to practise the interview problems you'll face in an interview.
I wish someone gave me this advice towards my career earlier, and this is probably the most important advice to receieve about graduating as a Comp Sci, so I thought I'd share with you what I have learnt.
Good luck in the future!