The majority of electrical installations carried out after 1966 should have been wired in PVC insulated cables and therefore full rewiring may not be needed. These installations may only need upgrading to bring up to date with current regulations.
Items often needing upgrading include:

Earthing and Bonding. There have been a significant number of improvements in this area to try and make electrical installations safer. Most importantly the main bonding of the Gas and Water services at the meter / main stop tap. Supplementary bonding of pipework and radiators in bathrooms.

Socket outlets due to them being installed on or in skirting boards. Regulation No. 522-06-01 no longer permits this practice. The skirting board is designed to protect the base of the wall and by mounting electrical accessories in or on it; they could easily be damaged by, say, a vacuum cleaner.

Old Fuse Boxes fitted with “Out of Date” re-wireable fuse. Although these type of fuses are still permitted by regulations, they do not offer the best protection to the cables installed and they do not offer any protection against fatal electrical shock. Re-wireable fuse (BS 3036) also give rise to an incorrect fuse wire being fitted and as we have often seen anything that may be to hand to get the circuit working again, such as a nail, a piece of copper wire, tin foil, etc… Some older fuse boxes are constructed of wood, which was commonly used as an insulator. But as we all know wood is also a combustible material and for that reason is no longer permitted near open electrical connections.