Yup, Themas has sussed it correctly - you would be advised to extract a Statement of Truth or a Statutory Declaration from the seller at this time, to demonstrate the 17 years continuous use of the 'new' access that you want - then in 3 more years you can go back to the LR with another ST of our own, which coupled with the document you acquire now gives you the magic 20 years.
You seem like a bright guy; have a read of the LR Practice Guide 52 here - it explains all.
http://www.landregist...des/practice-guide-52
Statutory Declarations have to be done in front of a commissioner for oaths, which costs; more recently the LR have allowed STs to be used - these are simpler and don't require witnessing by someone who is going to charge you for the privilege, so is much preferred. LR mention the use of their own form ST4 which I have found does the job adequately.
Obviously you don't want to be informing the owner of the land on either side of the 'barren' strip what is going on - the owner at any point up to the 20 year grant could chop you off at the knees and cut this access to you.