as I always tell people, just because you've not been asked, doesn't mean you'll not be asked in the future. If asked (by your airline or by immigration) you are obliged to show any documents, including onward or return tickets. They are fully entitled to refuse you if you don't have these documents. It's your risk.
As so many have said, make sure you get the correct test. LAMP tests are available at Heathrow Airport in London, but not many countries accept these (for example, Hong Kong does take them!). Most countries want RT-PCR tests, which take a lot longer than the LAMP.