Its an interesting question, but unfortunately I don't think it would change too much.
Firstly - by the 1890s you've already got vast suburbs in London. Take Lewisham in South London, for example. By 1891 the population was 94,000 ish. That was up double twenty years before, and from only 34,000 before that in 1851. By 1911 it would be 174,000. At times just south of the Thames in London was growing faster than Manchester and Liverpool combined in the late Victorian period.
Secondly - People wanted suburban homes. Speculative building meant that people would advertise properties as they were being built and just keep going as land was so cheap as
@Kevin Lessard says - the sprawl was just unstoppable. The idea of escaping the overcrowded and run down centre for an outer rim that was greener, cleaner, and embodied the growing separation between work and leisure that people valued in late Victorian Britain. Cheap train and later tram tickets by the 1900s meant that thousands upon thousands of Londoners could move in and out of the centre each day for work.
Thirdly - Victorians were often skeptical about apartment blocks. Many viewed them as distinctly 'European' in a bad way and disliked the idea of living on top of one another. With magazines and domestic handbooks for the middle-class pushing a vision of the perfect home as being clearly a detached house with a front and back garden. Also, they were not actually alone. There are very few apartment skyscrapers [as opposed to business based or hotel complex ones] in Western cities apart from those like Hong Kong, Singapore, etc where physical space to expand is geographically limited.
So whilst I think you might get a few more American-style skyscrapers in central London, its unlikely to change the nature of suburbia that was already well underway.