At Gloucestershire Airport we operate a booking system for training instrument approaches, which is a major part of our business.
We issue 30 minute 'slots' on the whole and half hours. This gives you time to do a join, 1 hold, the approach and missed approach procedure or 2 approaches....or any combination of the abvoe. All Instrument training is PPR and accepted on the basis that, if commercial traffic or arrivals requiring an approach due to weather turn up, the trainers go to the back of the queue. Additional training approaches are accepted if we can fit them in. We do our best, the more approaches we get in, the more money we make...but it'd not always as straightforward as it may seem.
Even if you elect to fly the approach under VFR, thereby removing our obligation to provide standard separation, we're still responsible for regulating the flow into the ATZ and 'sequencing' the traffic safely and expeditiously...and let's be honest...you're doing the approach to 'keep your hand in' i.e. flying predominantly by reference to the instruments and, subsequently not really looking out the window as you should be under VFR, so we'd treat you as IFR anyway
Another potential issue, which judging by your reference to 'Tower' on the ATIS, may apply here is the legal situation. Can't remember the ANO Article number, but the gist is "Providers of air traffic services are to provide an Approach Control Service when Instrument Approach Procedures are notified as in use" (...that's incidentally why you can't legally fly IAP's at a non-ATC airfield.)
If Shoreham don't always have an Approach rated Controller available for duty then the IAP's cannot be used.
There have been rare occasions here, during staff sickness/shortage etc. when we've had to 'withdraw' the Approach service because the ATCO on duty only has a Tower rating.
The 'Black Art' of Procedural Approach Control, particularly outside Controlled Airspace, is great fun....especially at night when everything's IFR!! Pity it's no longer mandatory to hold the Procedural Rating before progressing to Approach Radar...IMHO the newer generation of ATCO's are missing out on a skill which requires you to build a mental picture of the traffic situation. That said, I do get a bit scared when our Radar's u/s....
Hope this drivel makes sense to any non ATC types reading