I would not make any assumptions that something that is either possible or legal in the US with regard to either wiring or smoke alarms will also be legal/possible in the UK.
UK does not assume that most electrical work can be done on a DIY basis the way the US does.
There are relay devices With a similar function, but you can’t use the one that was linked to and meet UK safety codes.
Instead, you have to buy smoke sensors which are designed to have the ability to have a relay added, And there will be a relay piece specifically for the purpose of connecting to external systems, and it will generally slot into the smoke sensor itself, not into the mains.
Here is just one typical example:
There are lots of these, so you just have to check the specific brand and model of smoke sensor you are interested in.
Community members from the US should be aware that these kinds of issues come up frequently in the UK discussions, so please only recommend specific devices if you have verified that they meet code in the UK. 