This change is the latest in a series of steps recently taken by the UK including the acceptance of vaccinations received in more foreign countries and the significant reduction of the travel red list.
Alderslade said the change was a "major step forward that will support the desperately needed recovery of our sector."
The announcement comes a few days after the UK experienced their highest number of cases in a single day since late July, with 45,066 cases and 157 deaths.
The country continues to record the highest level of Covid-19 deaths and infections in western Europe.
Due to shared borders, Scotland, Wales and Northern Ireland have previously aligned Covid-19 related policies with England.
However, the Welsh government has voiced criticism about the replacement of PCR tests.
In a statement, Wales' health minister Eluned Morgan said the use of lateral flow tests along with the "radical reduction" of red list countries would "considerably increase" the risk of introducing new variants into the country.
Those who receive a positive result from the lateral flow test will have to self-isolate and take a free PCR test to confirm the result.
However, from October 24, those who return a negative lateral flow test will no longer have to take a PCR test within two days of returning to England, which can cost approximately £75(NZ$145) per person.
A list of approved providers, where travellers can order a lateral flow test, will be published on the gov.uk website from October 22.
According to Health Secretary Sajid Javid, the UK's high levels of vaccination meant they could "safely open up travel as we learn to live with the virus."
Transport Secretary Shapps said the removal of mandated PCR testing was significant for the travel industry. Shapps describing it as "a major step forward in normalising international travel and encouraging people to book holidays with confidence."
