Low ranked uni to a highly ranked university for MSc

I am an undergraduate student at the University of Winchester reading BSc Software Engineering. In my second year my median grade was above 90%, with my grades ranging from 100% to 72%. My A level grades were not strong due to severe Mental Health issues caused by the COVID lockdown.

I have been working 2 days a week as a software developer for half of my second year and am now also working 3 days on a different development job over the summer. I also have an AWS certification, have trained myself in methods in software architecture design and requirements engineering and have worked professionally with multiple programming languages and frameworks.

Would I still stand a chance of a successful application when applying to Russel group universities for a MSc in Software Engineering or Computer Science? Specifically please may I ask about Southampton, Exeter, UCL, KCL and St Andrews? I am concerned that the ranking of my university will cause my applications to be rejected.

Many thanks

Thank you very much, that is comforting to hear. I appreciate you taking time out to help me with this.

Please may I also ask when in my final year I should look to start applying for more competitive courses?