Screwfix lists type B and C (what happened to Type A)?

Always use Type B, unless you have a specific reason to use a lower
protection rating (you don't!). There is no Type A, although I'd like to buy
some if they made one. They'd be very useful for large pure resistive
circuits, such as cookers.

I have (it looks like) two switches for incoming power (LHS), plus an RCCD
(RHS).

You'll see that the switch on the left has the two handles connected
together. This is because it is a double pole switch that switches both the
Neutral and the Live at the same time. It should cut power to the entire
consumer unit.

So I presume that I could keep the lighting running with the power side off
whilst I connect in the new cables.

I wouldn't. There will be live busbars in the consumer unit, protected only
by your incoming service fuse. I wouldn't want to short that out by dropping
my screwdriver. Turn off the main isolator (left hand switch) before doing
any wiring up.

will almost any circuit breaker fit any consumer unit (CU was replaced six
years ago) because they are an ISO standard fitting, or is it a case of
loads of different fittings?

Most makes will fit most boards. However, many will claim that you should
not do so, or that it will invalidate the guarantee. If you are worried,
then buy Siemens ones, if you can find them.

Is it usual to have the incoming service split into 3?

Yes. Electricity is generated and transported around the country in three
phases, 120 degrees apart. Large industrial motors use all 3 phases as they
can maintain constant power throughout the mains cycle. A standard domestic
electricity supply uses one of the 3 phases selected at random by the
electricity company, often fused at 100A for a modern installation, although
older ones may be 40A or 60A.

With electrical heating installations, such as storage heaters, you would
typically have a 2 or 3 phase supply as they draw too much power for a
standard domestic cutout. So your guess is probably correct that you did
once have a 3 phase supply. It was probably all removed when all the Economy
7 gubbins were removed and a single phase meter installed.

BTW, I'm slightly worried by some of your questions. You might want to
consider doing the main wiring up of the circuits and then get an
electrician in to test and make the final connections. You need some very
expensive test gear to do the circuit testing, not a 2.99 multimeter from
Maplins.

Christian.