PhD mitigating circumstances

Hi I'm a 4th year MSci student about to start applying for PhDs. At the beginning of 3rd year (c. Oct 2022), I was diagnosed with a learning disability which I believe severely affected my performance in previous years.
I spent a lot of 3rd year trying to find a learning/revision strategy that worked best for me and ended the year with a 2.1 (~67%) which is a lot better than I've done previously.

I think I could've done better but I also faced some family tragedies that year (severe/terminal illnesses) which left me devastated and unable to focus at times. I was feeling so low I didn't even bother to apply for any sort of special consideration.
Although I didn't do as well as I wanted to in some of my modules, I have consistently done well in research assignments - especially in 3rd year. The lowest grade I received in a research assignment was 77% so I know that I have the potential to do well in a PhD.

At this point, I've learned quite a lot about which revision strategies work best for me and I think I have the potential to do well this year. I believe that I can finish the year with a high 2.1.

Now my question is: do you guys think there's any point applying to places like Oxbridge for a PhD. I know that I have very strong research skills, I have good references willing to vouch for me and I've had some relevant experience. I think that I have what it takes to do a PhD but unfortunately I don't feel like my grades have been a true reflection of my capabilities.

Has anyone had experience with applying for a PhD with mitigating circumstances?

TLDR; I want to apply for a PhD in Physics at a top UK uni but have had mitigating circumstances that have affected my grades in the past. I think that I could still meet the entry requirements but am wondering if extenuating circumstances may increase my chance of being accepted. I have very strong researching skills, have some relevant experience and should be able to get good references.

There is no simple answer to this one, but let me give a bit of background. When a student applies to an undergrad course with mitigating circumstances, there is clearly a risk involved. That student has not performed as well as they might have done so far, if you offer a place, it’s on the basis of a hope that their problems are behind them, and they will do better in the future. It’s a risk, but one that’s spread over a large cohort and lots of individual staff members. A few admission mistakes is balanced by helping other students with a worse start in life get a leg up.

For a PhD the entirety of the risk sits with a single supervisor or a small group of academics running a project or CDT. That makes people much more risk averse during recruitment. PhD funding is competitive and quite limited. If you as an academic “win” a £100k pot of money to fund a PhD, and you get to do that once every 3-5 years it really impacts your research productivity in a major way (good or bad). So in summary, yes, individuals may take mit circs into account, BUT, there will be much more attention on potential risk v reward from the supervisor. This is the place a strong reference from someone who actually knows you well and has seen your performance on an undergrad project can really matter.