2.1 Sufficient for Masters? (Computer Science)

I want to study for a MSc in CS in the future.

Places like Oxford, MSc CS or their Part-time SWE programme, or UCL's.
(Which is more likely to accept me, or is their SWE MSc also highly sought after?)

I have a 2:i (2.1 or whatever) from a RG uni. Had a few events happen at uni so now I tick the Reasonable adjustments disability boxes etc. Also tick all the low income, first from family in uni, BME, boxes etc.

Oxford et al ask for 1st class. Previous thread with the Oxford dept. stating that 2.1 students can still get in. However, that thread is over 8yrs old.

I have sent an email to course admissions to ask.

Any thoughts? I want to apply next year or in a few years, but it is a goal of mine.