There are aspects to the EICR that are not terribly great, but that board ( = fuse box = CU) is probably pre-1980 and if it is at all possible you should be changing it now irrespective of the results. There is an RCD in the white box but it looks not to be protecting any of the socket circuits, etc. If used for outdoor appliances, extension leads, etc, that is a pretty dangerous thing.
It might not need rewiring as such, if the cables really are in good condition, but given the age of that you will probably find there are not enough sockets in each room, or where you want them to be, same for lights or kitchen appliance locations. That alone might justify the extra cost of an actual rewire.
Do that before you consider new carpets or decorating! You might not want extra expense just now, but longer term it makes the house safer and increases the value should you want to sell in a few years time.