Yeah, it's probably this.
OP, I'm foreign, obviously brown, but I write and speak English to a good standard - not perfect, and have had no trouble. Although it's not my first language (it's my third , in fact). And my accent is obviously foreign.
in your case , your lack of success is likely more to do with your skillset. Unlike certain other countries a degree in the UK doesn't guarantee a good job. You're quite proud of your MA - rightly so, given the circumstances in which you've achieved it.
Unfortunately there are thousands of others with the same qualifications, chasing the same jobs, and with better experience than you. 4 years on, you're not a graduate anymore.
I've mentored and even worked with a lot of graduates who got a graduate job despite their English not being the best, they had something to offer. If you look at the threads on here many other people struggle to get grad jobs with minimal work experience.
I wouldn't say that there's no bias , In a sense that a graduate with perfect English might have more success than you. But having sifted through lots of CVs, so many 'native' speakers can't even write properly in their own language, and so many others, like me, are much better. I don't see this as a massive issue