The global financial crisis has a lot to do with it. A ton of the best talent in London were at startups and design agencies which went under; a lot of them went to the Government and did a really rigorous job; even though they've now moved on, the culture they put in place was bulletproof.
Yes, in recent years many top GDS employees have left[0].
Most common past 'companies' for GDS employees on LinkedIn are Department for Work and Pensions, Cabinet Office, Ministry of Justice & Home Office[1]. All the people I know of there used to work at the BBC.