You have old likely obsolete distribution boards, likely the larger board got a code 1 due to missing blank, that is easy enough to cure, however as to upgrade the question on need for upgrade is linked to 701.415.2 Supplementary equipotential bonding.
In BS7671:2008 it was allowed to reduce the bonding in a bathroom on condition all circuits in the bathroom are RCD protected.
So it hinges on the inspection and testing in the bathroom as to if RCD protection for lights is required.
The regulations are not retrospective, but some laws are, and the regulations follow new laws, so without reading all new laws hard to say what is allowed, however the EICR does not say if the premises are legal or comply with regulations, we have a series of codes of them code C1, C2, and FI are considered as fail.
Code C1 = Dangerous and there is little argument, if you can touch a live part clearly dangerous and likely can touch live part through the missing blank.
Code C1 = Potentially Dangerous and 230 volt electrical equipment is potentially dangerous so rather a silly phase, but most take the view if it was not considered as potentially dangerous when the British electrical system was changed to use the ring final during WW2 then it can't really be considered potentially dangerous now unless some thing has changed to make it so.
There have over the years been changes, from moving to TN-C-S earthing, to bathroom bonding, and over the years we have had some major changes, 1966 we had to include an earth wire to lighting, and the use of RCD protection has slowly evolved first for TT supplies, then supplies outside, and now near every circuit, and with this the installation equipment has also changed, in 1992 when I wanted to fit RCD protection as son had become a radio ham, I could not have fitted a metal type tested enclosure with type A single modular width double pole switching RCBO's and a surge protection device even if I wanted to, the units were not available. So I ended up with this
two old Wylex fuse boxes with the fuses swapped for MCB's and two RCD's feeding the fuse boxes. Over the years the RCD's have both protected and been a problem where they have tripped with no good cause, today's RCD's are half the size, and include electronics allowing them to be more resistance to spikes plus the SPD removes spikes, and today one would not consider fitting RCD protection outside of the main type tested consumer unit as simply no point.
But costs have also changed, those MCB's today cost around £11 each, a modern one from same firm £4.20 so often it is false economy to try to retain the old units.
As a home owner I can decide how far to go, and if as said I have a son who plays with radio I can go the extra mile, or if I do nothing but watch TV all day and do no DIY or hobbies likely to cause danger I can select to not upgrade, but not as easy for the Landlord, he has less control over what people do in his house, and he has to consider if he should provide protection for the occupants.
When things have gone wrong, even when one thinks hang on they saw it sparking why did they touch it, courts rarely blame the tenant it is normally the landlord who is blamed, so consider the court case, the electrician recommended fitting RCD's and the landlord did not fit them so when little Johnny did some daft action he died. Fitting the RCD protects you as well as the tenant.