At the moment, the venue can stick to the contract – if you cancel the wedding yourself, you’re breaching the contract and can’t get a refund. If the venue decides to cancel it closer to the time – because venues must still be closed and weddings still banned – you have to get a refund.
At the moment, it’s an annoying case of ‘wait and see’. Have you got wedding insurance? If so, they should be able to cover lost deposits etc if your suppliers have to pull out of the wedding if it goes ahead on 20th June. If the venue are still being tricky about it when you know they have to be closed on the wedding date, you can also get your wedding insurance company to step in. If you paid your deposit on a credit card, your card provider is jointly liable too – so you can always try to claim the money back from them, instead. There’s an article about coronavirus wedding cancellations here, which might be helpful!