On Thursday (8 July), the transport secretary confirmed fully vaccinated travellers will no longer have to quarantine when returning to England from countries on the amber list, with the new rules set to take effect from 19 July.
Alderslade described the move as "positive" and was "what the sector has been looking for".
"Opening up the market for the rest of the summer, this announcement will provide far greater opportunities to travel, do business and see family and friends, and enable many more of our customers to book with certainty. The summer season essentially starts here," he added.
EasyJet chief executive John Lundgren welcomed the plans, but slammed the government for sticking with "unnecessary testing".
"We have always said that vaccination is the key to unlocking travel and now millions will finally be able to reunite with family and loved ones abroad or take that long-awaited trip this summer," Lundgren added.
"But with unnecessary testing staying in place, more needs to be done. We do not want to see a return to flying being a preserve of the rich and expensive testing could sadly make travel out of reach for some this summer."
Stewart Wingate, chief executive of Gatwick, described the plans as a "small step in the right direction", but echoed calls to "remove other boundaries", such as PCR testing, for those fully vaccinated.
"At the very least, if tests are required, they should be the more readily available lateral flow tests or PCR tests carried out free of charge at an NHS facility, as has been done in France," he added.
"We would also urge government to urgently follow the lead of EU countries to ensure that internationally agreed, coordinated protocols are in place so that processes when crossing borders to other countries are as smooth as possible, with no unnecessary queues, checks or costs."
BALPA general secretary Brian Strutton said: "This is a good step towards the goal of safely opening up international travel, but there is still a long way to go. We need a sector specific financial package and an extension of furlough to stop skills being lost forever."
British Airways’ boss Sean Doyle said the airline was "pleased to see this common sense approach", but there is "more work to do".
"The government needs to quickly extend this to all vaccinated travellers, agree a reciprocal deal with the US, add more countries to the ’green’ list and reduce the need for unnecessary, expensive tests. This will allow the UK to catch up with other countries and send a message that global Britain is now, finally, open again."
Shai Weiss, Virgin Atlantic chief, described the move as a "positive announcement", as the airline prepares to work authorities to "ensure safe and seamless international travel".
"The announcement should now lead to significant changes to the ’green’ list from next week and further relaxation of testing requirements for fully vaccinated passengers of all nationalities arriving into the UK from green and amber destinations from 31 July.
"This approach is consistent with that taken by the US and the EU to fully vaccinated passengers, and will pave the way to restart of the essential Transatlantic travel corridor, without which £23 million is lost each day from the UK economy."