How can I officially prove that a Bitcoin private key is owned by an entity? I am the co-founder of an early-stage startup that aims to prove existence of various qualifications (academic, professional...) via the Bitcoin Blockchain.

In order to validate a piece of data, an issuer (say a university or other issuing body) would have to send a small transaction from their wallet which is managed by us.

Is there any way to officially prove (in this case in UK legislation) that a specific legal entity is in possession of a bitcoin private key and, therefore, to the coins associated with it? I know of a "statutory declaration" but is there anything more specific I can do?

Basically I would like to transfer ownership of the wallet to the customer, in order for myself to be criminally punishable if I upload qualifications to the Blockchain without their consent.

Is this at all possible?

Thanks!
A middle man trying to create a business around being a middle man with a technology thats supposed to remove intermediaries?

It seems like you could accomplish what you want with multisig wallet and counterparty.

In the example I have in mind, 

The issuer could create an asset that represents qualifications. The issuer could invite their practitioners to a 2-of-2 multisig address and send the asset to that address. 

Although we can't confirm if only those two parties have the keys, we can see where the asset came from (but it one scenario it can also be issued by the multisig address and never moved). We can rest assured that it would require both parties, one of which being the individual, to create a proposal to move the qualification asset. And these proposals will be rejected.

Another perk is that the asset can correspond to a centralized system.

Predictable, there's no place for your business in this mix, but that's probably the point, so I would like to thank you and your investors, in advance, for their charity in bringing this idea to the world. Should probably do an ICO