The change in policy for the post-arrival test will come into force from October 24, in time for families returning from half-term breaks.
Travellers who take a test at home must take a photo of their test and booking reference, and send this to the private test provider to verify the results.
In an interview on Sky News Mr Shapps accepted that the system will be “based on trust”, adding: “In this world nothing is 100%, and until now we haven’t been requiring any verification.
Mandatory PCR tests will be gone in time for October half-term! 👍🏻 for vaccinated adults and families seeking some winter sun abroad ❄️☀️
From 24 Oct take a cheaper lateral flow test on return, to make travelling easier and simpler for everyone 👨👩👦👦
— Rt Hon Grant Shapps MP (@grantshapps) October 14, 2021
“Of course, the system requires people to be honest, like so many laws in this country.”
The minister told Times Radio that the process will be “robust”, but it is “important that we have a system in place which is straightforward”.
The use of lateral flow tests will only be accepted for fully vaccinated arrivals who have not visited a red list country in the previous 10 days.
The tests will cost about £25, compared with a typical price of £75 for PCR tests.
Anyone who tests positive will need to self-isolate and take a confirmatory PCR test provided by the NHS.
Luke Petherbridge, director of public affairs at travel trade organisation Abta, welcomed the announcement, and urged the devolved administrations in Scotland, Wales and Northern Ireland to adopt the new approach.
He said: “Costly tests have been a huge barrier to people travelling so we hope this will help make overseas holidays much more accessible.
“Brits are desperate to catch up on their much loved and much missed foreign trips.”