Well I'm back now and can give you some disheartening opinions.
Your consumer units/fuseboxes are pretty old now. That brown Wylex, with the bakelite cover and mahogany frame, has been obsolete a long time (I fitted my first White ABS Wylex 30 years ago, so I would guess it is older than that).
Although they were very popular after the war, and no doubt good at the time, the switch does not carry many amps (and is probably worn out by now) and the terminals inside, especially the earthing block, is too small for todays standards. It may also have rewirable fuses, which are frowned upon now, and rather troublesome if you ever have one blow.
The arrangement of main earths looks suspect from here, though of good size, and the meter tail with sticky tape is worrying - this might have been put on to cover damaged insulation.
That tail will be fused at 80 or 100Amps, and has no switch to turn it of in case of probs. The 45A CU is not as old, though I think I can see signs of overheating on the fuse carrier?
The rest of the installation is rather old and untidy (I'm not blaming you)
and I believe there is now a requirement for a fireproof barrier between the gas meter and the electric meter; there should certainly be a bigger gap than I can see between the brown consumer unit and the pipe beneath it.
If the bits we can see are old and scruffy, it's a fair bet that there are other aspects that also need attention. In an old house you usually find there are nowhere near enough sockets, main and supplementary earthing are poor, lampholders are cracked with heat and age, switches and sockets are loose and worn, and often you will have metal switches or lighting fittings with no earth.
If you have recently moved in, and are spending money on the house, you should be thinking about renewing the electrics rather than patching them up. That means you will need a qualified professional to replace the old boxes with a nice new consumer unit, I'd suggest a split-load 12-way, you'll be surprised at how easily you fill it with circuits, and how little extra a big one costs compared to a little one. Getting a professional in also means he will test your existing circuits before re-connecting them, and although there may be scope to re-use some of the old circuits, if money is really tight, you will get a better job, really, by replacing the old lot. It is possible to replace a CU yourself, but you will have to pay for testing and inspection, and unless you are skilled enough to do everything right first time, it may end up costing you more.
Looking on the bright (!) side, the advantage of doing it now is that as you work through the house decorating and refitting, you will be covering up the new chases and decorating round the fittings, this is much better than having to chop them out and mess up your new tiles wallpaper and flooring.
How do you feel now?