Chris - the current register will only confirm who now owns it
The Transfer will confirm your name(s) and the name(s) of your buyers also which confirms you did own it and they purchased it/you transferred it on the date of that deed
If you want a copy of the register showing you as owners then that's form HC1 - see the part entitles 'historical registers' on the first link
Get information about property and land: Search the register - GOV.UK
But as I posted all about what proof the council want/will accept so worth asking them to confirm if you can - they won't want all three or more I suspect