I have a Yale HSA6200 wireless alarm system – and I think it quite good (as do a few others reviewing it here):-
https://www.screwfix.com/p/yale-hsa6200-wireless-alarm-kit/97114?dclid=CLK46__989gCFWmo7QodixwJZg
I think I bought mine from Wilkinson’s for £100 a few years ago.
Although the system is fairly limited, with only 2 door sensors, 2 PIRs and a key pad – you can add more, including a remote fob for arming/disarming (much better than using the key pad).
I’ve never had problems with false alarms, and with the system set to detect someone entering on the ground floor, each night I use the remote to arm the system on retiring to bed.
The only downside is that the alarm box batteries (4 D size cells) need replacing every 2 years or so, requiring accessing the unit mounted high up on an outside wall.