RCCB trips and causes sockets to lose power, but lights, etc. don't lose power
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.