Hi Rafaelle!
Accents are so interesting and so varied, which can make them a bit of a nightmare for language learners. One of the difficulties that you can encounter is that actually most native speakers don't know much about accents. Actually, that's not completely true: often we can intuit a lot about a speaker from their accent, but it's very difficult for us to talk about what we can hear, and lots of the terminology around accents can be vague, which leads to lots of confusion and disagreement!
To be able to answer your question, we first need to establish what we mean by RP. Lots of people think that RP is the "standard British accent", and lots of English learners are told that. This isn't really true. This YouTube video gives a really good introduction to the reality of RP:
https://www.youtube.com/watch?v=PcIX-U5w5Ws
Now you've watched that, I'll try to answer your question.
Here's a fairly common example of how people talk about the difference between RP and cockney accents:
https://www.youtube.com/watch?v=7_FtnOTLkSs. Actually, the cockney accent has been mythologized too. Lots of people think that cockney is a common accent and is just a less formal "standard" accent. It's not -- it's actually very specific to an area of East London and a specific economic background. However, aspects of this accent have been incorporated in what is known as Estuary English (
https://en.wikipedia.org/wiki/Estuary_English) which is spoken over a much wider area, but it often mistakenly referred to as "cockney".
In the RP vs. Cockney video, I think it's important to point out that the woman's RP accent doesn't sound at all natural.
In Benjamin's video, his accent is "kind of RP but not really" and he notes he has some aspects of Estuary English in his accent. The two most common features of this is "dropping ts"/glottalizing at the ends of words and velarizing dark /l/ sounds (when they start to sound like /w/).