Lord Callanan said he would urge his counterparts to "do all they can to reduce queues and allow travellers to get on with their holidays".
European Union member states have until October to implement the checks in full, adds the paper.
"While border arrangements for Schengen countries are not in the United Kingdom government's control, I will be speaking to my counterparts in Portugal, Spain and Italy to urge them to do all they can to reduce queues and allow travellers to get on with their holidays".
Travellers' details now have to be run through databases to see if they pose a threat. "National border authorities and agencies have thus had lots of time to prepare and put in place the necessary arrangements and staff", he said.
"This Sunday is set to be the busiest day of the weekend with over 104,000 passengers expected to arrive and depart through both terminals", the spokesman added.
Some passengers have missed their flights or been forced to queue for up to four hours while leaving or arriving for their holiday, Europe's largest airline association has warned.
Airlines for Europe (A4E), a coalition of carriers such as British Airways, EasyJet and Air France-KLM, have issued a statement criticizing several major airports in the continent over "huge delays".
New border controls have left some holidaymakers queuing for up to four hours at Europe's main airports.
"Airports like Madrid, Palma de Mallorca, Lisbon, Lyon, Paris-Orly, Milan or Brussels are producing shameful pictures of devastated passengers in front of immigration booths, in lines stretching hundreds of metres".
Airlines For Europe, a group which represents carriers including easyJet, Ryanair and British Airways' owner IAG, said that compared to previous year some delays had increased by 300 per cent and that some passengers had missed flights. However it is feared the situation could get even worse in the coming weeks, as the new regulations have not yet been fully implemented.
Member states have a six-month period ending 7 October to introduce the changes.
Many travellers said they were unaware of the long queues and the extra time needed to get through some airports.
"We have also hired additional security staff this year to help cope with growing passenger numbers".
"More checks can lead to more delays, and that is the price for security".