I think it's just that the bandwidth of the microwaves is not much by today's standards. It was capable of 150,000 simultaneous telephone calls, which is something like 10Gbs. It may be that modern numbers were higher, but possibly not much as you have to share the microwave spectrum with other uses. In a fibre you get the whole optical spectrum to yourself, so you can achieve much higher speeds. You can also run many fibres in the same ducting and increase bandwidth that way.
For backup / resiliency you just run more fibres via different routes.
I wonder how many of them were originally set up there because of proximity to the tower and its communications links. Other than that, isn't Fitzrovia basically UCL and early 20th century novelists? Although I suppose there is Broadcasting House over on the other side.
Maintaining redundant fibre links (which exist) would likely be cheaper than maintaining a decades-old microwave system (I would wonder if they even have the appropriate spectrum licenses anymore, anyway).