You send it as a PDF attachment by email. There is no better proof of delivery than an email.
Signed for post is definitely not reliable. If the recipient refuses to sign for it, all you have is proof of non delivery.
If you insist on posting anything, use the free Certificate of Posting from any Post Office. The Interpretation Act 1978 covers the "proof of posting" for deemed service of a letter in the UK. Specifically, Section 7 of this Act addresses the concept of deemed service, stating that unless the contrary is proven, a letter properly addressed, prepaid, and posted is deemed to have been received in the ordinary course of post.
In practice, this means that if you can provide proof that a letter was posted (such as a certificate of posting from the post office), it is generally assumed to have been delivered unless the recipient can provide evidence to the contrary.