I think it depends if you are willing to consider a non-London lifestyle. If you absolutely want a London lifestyle, and nothing else will do, then I think the move will not work.
Cardiff is a smaller city and it is going to be very different. Not necessarily better or worse, just very different- it is "horses for courses" as they say. What works for others may not work for you.
I've not lived in Cardiff so can't really comment specifically on the city itself.
However, I lived in London for a year. I enjoyed it for what it was, but would not choose to live there long-term. I like to visit for short spells but that's about as far as it goes. I much preferred living in Edinburgh, loved it at the time and have many fond memories. I live rurally now and I don't think I'd ever want to move back to a city environment TBH. But there are many people for whom my lifestyle would be their idea of hell- neither of us would be wrong.
I have an acquaintance who moved up from London and spent most of the time pining for London. He could find little to like about anywhere that wasn't London and spent all his time looking for faults rather than positives. He never really gave it a chance, which was his prerogative (and I understand he wasn't particularly happy), but listening to him go on and on about London and how awful anywhere but London was did get a bit boring. And I have to say, he tended to get people's backs up with "well it's fine, but London has so many more/better ......(insert place/acitivity/restaurant etc)". And "well London is more multicultural, most people here are so parochial/small minded" etc did not help much either. He did move away (to Manchester) and I hear feels pretty much the same way about Manchester as he did about Edinburgh.
Of course, some places are more parochial than others and some have more ( or perhaps just more overt) racism than others- though I have to say that I came across a reasonable amount of both racism and small-mindedness in London/SE England so I don't think these traits are exclusive to "anywhere outside London". I do find it slightly insulting I have to say, but there you go.
What I'm trying to say, in a rather long-winded way, is that it is going to be very different and you are going to have to be prepared for that. If you are wedded to a London lifestyle and cannot see anything outside of that, then you do need to look at staying in London but living in a cheaper area if your health means a change in finances. Because moving with a mindset that "London is the be-all and end-all" will end up in disaster.