The above post is sound advice.
In the heel of the hunt, a planning permission relates to property in any case, and not to the applicant, so from this point of view it does not matter if its you or the prospective tenants who applies.
The main thing that will expedite the processing of the application is the amount and quality of information which is originally submitted. In cases like these, it is likely that the planning authorithy will request details of ventiulation, a detailed kitchen layout, details of opening times etc, so it would be prudent to include these in the original application in order to avoid further information request.
Try to find a similar successful application to the same authority in the recent past, and ensure that all the information requested as further information is included in your original application.
You should also note that an application for a fire safety certificate will be required for the change of use, and this also takes a minimum of eight weeks to process.