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I have a ring mean. off a twin 13a socket there is a fused spar, off it is a house alarm.

I wanted to know if I could spar of a spar to run a light 1.5 cable (ceiling rose)

If so what amp fuse etc...

I spur must feed only one item. However a radial can feed many items. What is the difference between a spur and a radial? A spur is feed by a fuse too large to protect the cable and it is the fuse at the socket end in the plug that does the protecting. With a radial the cable is protected at the origin. So where a cable is connected to a ring main using a fused connection unit it is a radial not a spur.

Spurs are also limited to a max of 3 meters.

So all you need to do is add a fused connection unit and make it into a radial.

However the whole idea of tagging on to an alarm system rings alarm bells. I know that many an alarm supply has been fitted by the so called alarm engineer and often the guy doing the work has not been trained even to electricians standards never mind an engineer. When asked what the earth loop impedance is they look at one with a blank expression.

So before utilising any of their work I would want to fully inspect and test and since you don't know the fuse size to use I would not think you are able to do that.

As to fuse size the standard ceiling rose is rated at 5A so that is normally maximum for any lighting circuit. Since 5A is not a preferred size normally one would fit a 3A fuse where a fused connection unit is used. But for most lamps up to 230W a 1A fuse is big enough. So if the alarm is supplied with 3A fuse you may wish to use a 1A fuse so any fault on lamp will not stop alarm from working. But normally 3A is size used.

You can't spur off a unprotected spur!
But you can spur of a fused connection unit (fused spur/FCU).
Can you not take the light from the lighting circuit?
But I would normally rate the fuse in a fused connection unit (FCU) for a light no more than 5A, you can then use 1.00mm cable.
If this is done in a special location (bathroom, outdoors] or kitchen, notification to building controls is needed.
Otherwise it will be in most cases considered minor work, this is not notifiable. But still should be issued with at least a Minor Works Cert or even a electrical installation cert.
This means the circuit will need to be inspected and tested and results documented.
You may also need the addition of RCD protection for at least the part of the circuit that has been added, if this is not already offered to the circuit from the consumer unit. This can be done by using a RCD protected FCU.

a spur is wiring that tees of from either a ring or a radial circuit. (see BS7671 part 2 definitions)
App 15 of BS7671 explains it all.
an unprotected spur from a 2.5mm ring must be 2.5mm and only feed one outlet, no mention of length.
if a spur is is protected by a 13A fuse in a fused connection unit it may be wired in 1.5mm and has no limit to the number of point it can feed.
a protective device protects the cable, that's all.