I've always sent it by regular post and never had a problem with lost bundles (famous last words!) and have no plans to change it at the moment. I've tried to arrange electronic transfer but we have a 100MB limit on attachments, so can't do it without splitting the appeal response into several pieces. Arguably there is more risk of that being intercepted or going astray that a posted bundle.
The current DPA allows disclosure in legal proceedings and I don't think this will change. Although there will be more emphasis on documenting information held there should already be an audit trail as required by GDPR, in that you will have a benefit decision, a revision request, a reconsideration and an appeal to the tribunal. The appeal response by nature has to include all relevent information, so I can't see a problem there, unless I've missed something. The new rules also include processing to meet a legal obligation, so I think from an appeal submission point of view there should be little change.
https://ico.org.uk/for-organisations/guide-to-the-general-data-protection-regulation-gdpr/lawful-basis-for-processing/legal-obligation/
