Firstly, the cable coming into the meter box must be at least 25mm I would be extremely surprised too see a 100 Amp protection fuse in that service head, given it's age. At this time, very little other power is being used, so not much chance of over loading the main fuse then.

Thinking of having an EV charger installed and I need some advice. Although I don't know for sure I suspect I have a 60amp main fuse and 16mm tails.There is nothing written on the Fuse so don't know for sure but my house was built in the 1970s and has never had any high powered equipment except a cooker so there is no reason to think it was ever upgraded. Somebody with better experience in domestic electrics can offer some advice, but here is my view on what I see.As I understand it I can have a charger with a 60amp fuse but it will have to be restricted to 16kw which defeats most of the purpose. So really I need it upgraded to 80amp or 100amp. If I want to get the kit upgraded as I understand it there may be several stages:

But upgrading to 100 Amp fuse is now recommended, due to the increased demand of other electrical appliance we all are running these days !. Make a personal decision what you think your requirements are likely to be based on that and let the electrician know who will then use a diversity calculation (proportion of theoretical total load that is likely to be on at once). Its their number, or actual monitoring, that is the one that decisions will be based on and whether DNO are in same ball park. At end of day, its what you have connected and use, not size of house, number of bedrooms/occupants etc. There is no form of junction between my meter and the consumer unit (which is quite new) so assume stage 3 will not apply since presumably upgrading the meter tails will have to involve a new connection all the way to the consumer unit so nothing left for an electrician to do

80 Amp Fused Main Switch Specifications

You just have to give a bit of thought to what and when, you will be placing a high demand on the system. Network Operator is responsible for upgrading the fuse and, if necessary, the cables running into the house They are very likely to upgrade the size of the meter tails and install a 100 amp isolation switch at the same time.