Many cases boil down to the analysis of digital devices. Indeed the recovery of messages from digital devices can often be, depending on the stage of investigation the difference between charge or no charge and conviction or acquittal.
If you are certain evidence was once on your device it may well be well worth the money to have the data from these devices forensically recovered. If the device is in your custody then its simply a case of engaging a digital forensic analysist to do the work.
If the device is in the custody of the police (maybe in the endless queue for them to download the device) then there are some options. Both options would usually involve you engaging a solicitor for some pre-charge representation and having them trying to convince the police it makes more sense for them to send the phone to an independent analyst (at your cost) in order to speed up the process.
The police are not obligated to agree to this although if they are wanting to get cases finished it would be in their interest to do so.
The police could simply say no. However, if they say yes they could say yes in one of two ways. They could be agreeable to courier the device(s) to the independent expert or they may insist the expert comes to their location. Almost certainly it would be conditional that the results are shared with them.
This would unlikely be a matter that the police would engage in conversations with yourself about. As such as well as the fees for the digital expert you would have legal fees to pay for the pre-charge representation and coordination from a specialist solicitor in pre-charge representations.
Currently via a couple of ongoing cases we can recommend Evidence Matters in Milton Keynes as been very responsive. Their details can be found via the link below.