Unsurprisingly, your installation is old and needs rewiring. There may be parts that can be salvaged, but it will be simpler to renew the lot.
You have a Wylex Standard CU with rewirable fuses (or possiby an own-brand copy such as Newlec). It dates from about the 1970's and is not up to current standards. We can assume that the cables will be of similar age and, although not degraded, they are likely to have missing sleeving and grommets, possibly no earth connections in lighting fittings, and far too few socket outlets. It's a 6-way so it probably started out with circuits for upstairs lights, downstairs lights, upstairs sockets, downstairs sockets, immersion heater and cooker. The cooker fuse would originally have been 30A and in your case has been replaced with a B40 which is not correct on that model. I hope this is not being used for an electric shower because the CU is unsuitable. The label under the main switch may explain.
The tails have been renewed, I can't see the main bonds but very likely they need renewing. An external RCD has been added, in such a way that if (say) the kettle trips it, all the other circuits including lights will go out. This is not now considered good practice, and is dangerous to anyone up steps or carrying a hot pan. There are probably other defects common on an old installation, such as DIY spurs, outdoor lights, and extensions.
An Electrical Installation Condition Report by a qualified electrician might take half a day or so and cost a few hundred pounds, but I think that an experienced person would be able to size it up sufficiently within a couple of minutes and save you the money.
If you electrician agrees, it is sometimes possible to add a new, large size of modern CU and to connect new circuits to it individually as they are installed. For example you might start with kitchen sockets, cooker and downstairs sockets.
I don't recommend installing a new CU and trying to transfer your old circuits into it. They would have to be tested to modern standards before it was permitted to go live, and some or all of them might fail test unless they were expensively rectified. Meaning you would not have working circuits until it was all completed.