The airport initially introduced the cap on daily departing passenger numbers in June, which it said has since "slightly reduced" numbers, bringing them into line with available resources.
"There has already been an improvement in punctuality, shorter waits for bags to be delivered to reclaim halls and fewer cancelled flights," a spokesperson said.
"Heathrow is keen to get back to operating without a cap as quickly as possible, but that is dependent on teams across the airport, notably some airline ground handlers, achieving sufficient resource levels."
However, last month, Menzies Aviation said the government failed to listen to ground handlers warning of a crisis at airports once the pandemic ended.
The call comes after Heathrow saw one million passengers depart the airport in the 10 days leading up to Tuesday (2 August).
Heathrow chief operating officer, Emma Gilthorpe, said: "My colleagues and I are thrilled to welcome so many passengers back to Heathrow again after two years of Covid cancellations and empty terminal buildings.
"The pandemic has been rough on the travel sector, but as we emerge and ramp-up operations, everyone at Heathrow is working hard to get you on your journeys.
"We’re focussed on getting back to giving you the excellent service you expect every time you travel, and by following our top tips – including ensuring liquids are packed correctly, you arrive on time and you have the correct travel documents – you can help us get you into holiday mode this summer."