Rightstuffer,
If they're not too busy they will usually let you through. A polite call on 129.55 usually reaps the dividends. Make your first call 'Luton Approach, G-ABCD for zone transit' and they will prioritise you over LARS requests (which I guess that they will continue getting even after the LARS is defunct).
Try to choose a routing that overflies the field at 2,400ft and they will often give you an on-track transit without having to bother about the CTR entry-exit points (more useful for those heading down towards the east of London). There's a 5km vis and a 1,500ft AGL cloudbase legal minimum for transit, however they may internally operate higher minima than this.
Finally, if you're IMC rated, file IFR at 2,400ft and they should let you through under IFR with no minima (and will keep you seperated from their traffic)!