There's at least one case back in the 80's when the mobility clause was tested at an industrial tribunal after a member of NATS/CAA staff resigned when posted from a regional part of the country to West Drayton. Some of the legislation will have changed a bit since then but at that time the tribunal considered only whether or not the application of the mobility clause was fair and reasonable. Its main consideration when doing that was whether there were good and legitimate business reasons for the move. Unfortunately in that case the tribunal ruled against the individual even though to some of us the business reasons seemed rather weak and obviously contrived. A rationalisation of centres is a far stronger business reason than those considered reasonable back then.
It is also worth bearing in mind that if your place of work is closed down the company actually has an obligation to consider re-location to avoid redundancy.
During the Field Engineering move to Spectrum House in the mid 90s there were some staff with a similar negative equity problem. It didn't affect me so I didn't pay much attention but I think the interest free loan was the eventual concession there.