This is a quite a complex topic.

Arc Fault Detection Devices (AFDD’s) are now recommended in the UK wiring regulations (BS7671) .. not mandatory. 
AFDD’s have been in use in the USA and some European countries for a while and they do protect against some fault types that our current circuit breakers (RCD’s, MCB’s and RCBO’s) don’t. They look for excess but not extremely high fault level currents which have the capability of causing arcs of power which can have a very high temperature and potential cause a fire without tripping the protection. 
 

One thing they are not so good at is detecting an arc fault in a ring circuit .. which is the most common circuit type in the UK. Our historic method of wiring is contructed to be robust, delvering power from both directions into the ring and so series arc faults are not seen although parallel arc faults are.

The AFDD’s also do not have a prescribed test device to check if they are operating correctly unlike RCD’s which check for Earth Leakage currents - an RCD tester is a key test device which every electrician who signs off a wiring scheme owns. 
Back to the question of should you get this installed .. possibly. There are test ‘buttons’ on the device but these just check the mechanical part of the trip, not the arc detection part. Some also have what is called an auto test which tries to check the trip capability on switch on/start up but I’ve yet to understand the manufacturers validation of this.

So .. ask your electrician how they would test that the device is operating and see what they say. 
AFDD’s will become part of UK systems in the future but personally I believe that they are in their infancy for trust and safety capabilities. Even with the level of fires we see caused by electrical appliances in the home. Are other countries who use these AFDD’s any less afflicted by house fires? I do not have any data to prove this.

Do I have AFDD’s installed myself? No, not until I can verify that they can detect what they are meant to.