Interestingly, I think the implosion of chain department stores in the US is linked far more to growth of online sales (even though, online sales are far higher in the UK) and overbuilding of retail capacity. The UK is seeing demographic/infrastructure changes with greater suburbanization.
Stores that are in out-of-town retail parks, more like US strip malls, are actually doing very well. One example is Next, a big clothes retailer, they used to have a lot of high-street/inner-city locations but moved stores out-of-town, and they are doing quite well (they also have a very nice business online, they even do third-party fulfilment from their warehouses). And there are lots of new chains focused around retail parks that are growing very fast.
Online is definitely a factor that is shrinking the overall offline retail market. But a lot of these department store chains started having problems in the 2000s, and just imploded in the 2010s. The comparison with the US is very interesting though.