[JMT1985]

Admittedly I'd forgotten about BGT's frequent set changes. Wasn't the last one before thr current arrangement quite 'theatrical' in a way - possibly the series after the London Studios closed so they were in a new home (Elstree?) that year?

X Factor did seem to keep that set for ages with the odd tweak here and there like Strictly do (changes from light boxes to more screens, expanding the walkway, a satellite stage at one end of the walkway for one year), with bigger changes elsewhere each year. I think the year the set finally changed (2017) - again due to the London Studios closing) - was the first time since 2010 that all judges and host from the previous year returned. And that year brought a new format - the Prize Fight! - before they went 'back to basics again.....

Sorry to be picky and pedantic but The X Factor never used The London Studios on the South Bank, they used The Fountain Studios in Wembley from 2004 until 2016, with The Fountain Studios closed down. 

The change in 2017, was when they moved to LH2 Studios in London, which mean they needed a new look. 

Strictly Come Dancing had been using BBC Television Centre studios, especially TC1 since they started in 2004 until the end of the 2012 series.  When the BBC closed down Television Centre after selling it in 2013 and a redevelopment of the site was about to happen from spring 2013, they looked to their next door neighbours at Elstree to help them, and agreed a deal with Elstree Studios to use one of their George Lucas Stages, currently George Lucas Stage 2 as their home for Strictly.

The move to Elstree saw a revamp of the set, as they went from using a 10,800 Sq Ft TC1 at Television Centre, to the much bigger 15,770 Sq Ft George Lucas Stage from the 2013 series onward.