A property record is only worth keeping if you control who reads it. So here is the whole picture.
By default, nobody
Your record is yours. Estate agents, insurers and lenders do not have standing access to it, and there is no setting that quietly grants it.
Sharing is something you do, per recipient, and the privacy notice sets out who those recipients can be and what they see.
When you do share, it is logged
Every read of property-record data by a professional organisation is written to an access log. Which organisation, when, and what they looked at.
That log exists for you rather than for us. The point of a record that outlives your ownership is that it can be shown to people, and the only way that is safe is if showing it leaves a trail.
Time-boxed, and revocable
A share is not permanent by default. It has an end, and you can end it sooner.
This is the part people find surprising, because the normal experience of sharing property information is that it leaves your hands and you never hear about it again.
What it costs
Property-history reports are free for signed-in users. What a report shows is governed by your sharing consents, so the same report shows different things to different people, which is the correct behaviour and occasionally a confusing one.
If you want to see the shape of it before deciding anything, there is a sample record at tradelynx.co.uk/demo/homelynx-passport.