Several times in the last month, we have experienced small power surges that cause the circuit breakers to trip. Most of the time this has been the "sockets" circuit breaker, however 15 minutes ago the RCCB "protected circuits" tripped, while the other circuit breakers remained on. During this the "sockets" lost power, but lights, and the rest of the electrical system did not go off. Is this unusual behaviour? From what I've read, if the RCCB trips, the entire electrical system is supposed to stop working.
Yes this is normal.
Under the 16th edition IEEE wiring regulations (introduced in 1991, superseeded in 2008, there were amendments, but I don't think any of them are relavent here) in TN installations* RCD protection in normal domestic situations was only required for sockets that could be reasonably expected to supply equipment outside the equipotential zone**. Interpretations of this varied, but in practice it meant that at least all downstairs sockets and frequently all sockets ended up being RCD protected.
Some houses were wired with a RCD covering everything but this was frowned upon because a single fault could leave the whole house in darkness.
It therefore became common practice to fit "Split load" boards where some of the circuits were on RCD and others were not. Exactly what got put on the RCD side was quite variable with some electricians putting everything except lights on the RCD and others only putting sockets and showers (I don't think an explicit requirement to put showers on the RCD but it was widely seen as a bloody good idea) on the RCD side. This appears to be the situation you have.
Since the 17th edition practically all domestic wiring needs to be on a RCD. On cheaper installations it was/is common practice to use a consumer unit with two RCDs so you only lost half the stuff when a RCD went out. Higher-end installations would often use "RCBOs" which combine the functionality of a RCD and a MCB and allow each circuit to be individually RCD protected. Until recently these were pretty expensive though.
There is no compulsion however to upgrade your existing installation to the 17th or 18th edition regs. Heck there isn't actually an explicit legal requirement to follow the IEEE wiring regulations (aka BS7671) at all, just a requirement that “Reasonable provision shall be made in the design and installation of electrical installations in order to protect persons operating, maintaining or altering the installations from fire or injury.”. Most electricians however will insist (and may be bound by industry schemes they are a member of to insist) that any new work is done to the current edition. In practice this means they will want to RCD protect any new wiring when modifying an installation.
* in a TT installation everything needs to be RCD protected, but sometimes with RCDs that have a higher trip current.
** I think there may have been some requirements for RCDs related to swimming pools and marinas as well, but those wouldn't apply in the vast majority of domestic installations.
“Split load” consumer units are quite common in the UK.
On a split load unit, approximately half of the MCBs run through a RCD and the other half can either run through a second RCD or may not be RCD protected at all.
The idea behind it being that an earth leakage fault tripping a RCD protected circuit doesn’t take out the supply to a whole house - for example a lighting circuit tripping the RCD wouldn’t then also take out the sockets circuit feeding the freezer.
Normally outlets and lights are on separate breakers. The rationale behind it is that if you plug something into the wall and it trips the breaker for whatever reason (e.g. faulty wiring, short circuit), the lights will still be on so that you can see how to get out of the room.
If a RCCB trips, then the outlets connected to it will stop working as well. Lights should remain on if they are wired separately.