No, not anymore! HMRC have finally accepted that digital copies of invoices, receipts and your business records are acceptable.
There are some great apps and scanners around that can help make this process really easy, just make sure wherever you choose to store your digital data that it is secure and reliably backed up.
How Long Should You Keep Copies of Your Invoices and Business Records?
You must keep your invoices and business records for 6 years.
Learn my own recommended process for scanning and storing copies of your invoices and receipts in my blog How to Organise Your Business Receipts.