I suspect that you'd either have to pay for this data or compile it yourself from various sources such as the Land Registry
However you may find the GetAddress site useful:
https://getaddress.io/
You may also be interested in the fully searchable UK postcode database I uploaded yesterday:
https://www.access-programmers.co.uk/forums/showthread.php?t=295233
This uses the freely available UK postcodes dataset from
www.doogal.co.uk
NOTE:
If you get a free API key from the
GetAddress site, you can download a full list of addresses for a particular postcode in
JSON format
There is a limit of 20 API calls per day
In theory you could combine that with the list of postcodes I got from
www.doogal.co.uk to get the dataset for the whole country BUT:
a) you'd have to pay for a licence allowing additional downloads - up to 5000 API calls per day
b) it would take forever to download
There are around 2.5 million UK postcodes (not all in use) so at 5000 per day it will take you 500 days .... AND the dataset will be mind boggingly huge
If you do find a freely available data source for what you want, please post the link here
UPDATE:
This site may also be useful
https://www.hopewiser.com/address-postcode-finder
It offers a similar feature set to GetAddress - a limited number of free downloads then you have to pay.