Yes, all LHR runways have MLS as well as ILS.
Although the advantage of MLS is only realised during LVOs, BA and LHR ATC agreed some time ago that MLS-equipped aircraft should use MLS as the default landing aid in all conditions. Reasons include controller and pilot familiarity with r/t terminology, use and limitations of the equipment and practice in applying the reduced spacing required for following aircraft using MLS.
The intention is that MLS procedures and terminology become so 'normal' that during LVOs no difference from 'normal' is required.