Not sure, under th terms of the lease agreement, if the UK has that authority. In fact, it was a particular point raised by the House of Commons that, when the renewal of the treaty became due, that such restrictions be added - but I am unable to find any document or report that any such restrictions were agreed prior to the lease renewal automatically rolling over in 2016.
https://publications.parliament.uk/p...7/37704.htm#a3
While the 1966, 1972 and 1976 Agreements relating to use of Diego Garcia impose obligations on the US relating to use of the Territory[[url=https://publications.parliament.uk/pa/cm201415/cmselect/cmfaff/377/37704.htm#note25]25] and make provision for (amongst other things) the exercise of criminal jurisdiction, employment of personnel, customs duties, access to the island, and conservation of flora and fauna, they do not impose any clear requirement upon the US to seek permission for a highly sensitive activity such as rendition, or even to support combat operations. The requirement which the FCO referred to in the extract from evidence to the previous Committee, cited above, appears to be entirely informal. This seems to us to be an unsatisfactory gap in the UK's formal oversight of the use of Diego Garcia by the US for defence purposes.
17. We believe that steps need to be taken to restore public confidence that the UK exercises effective control over the British Indian Ocean Territory. We recommend that, if the 1966 Agreement on Availability for Defence Purposes of the British Indian Ocean Territory is to be rolled over from 2016, the text of the Agreement should be revised. It should specify that any extraordinary use of the US base or facilities, such as combat operations or any other politically sensitive activity, requires prior approval from the UK Government; and it should state explicitly that the British Indian Ocean Territory should not be used for rendition unless authority has first been granted by the UK Government, on a case by case basis.