Peel says more big ships will come to Mersey as £400m terminal proving its worth
He said: "I have every confidence in the weeks and months ahead that you'll see the volumes here continue to grow.
"We've been having a number of very high-profile discussions with the shipping lines and genuinely we're at a point now where we've identified a couple of services we think could fit very well with Liverpool.
"We have been working with one of the lines on one particular service. The last meeting was only a few weeks ago. The meeting was opened up by this particular line and said 'we have never worked so proactively with any other port company in the way that we have with Peel Ports'.
"We've been able to jointly identify some real opportunities between us."
And he added: "If we can retain those two services here or secure this other that I'm referring to, it will have a significant impact on jobs and the local economy."
Peel Ports opened the Liverpool2 container terminal in late 2016. It is designed to welcome the world's largest container ships which were too big to fit into the port’s existing docks but can now sit in the river with Liverpool 2's cranes above.
The company says it has always planned to grow business at the terminal gradually rather than welcoming giant ships from day one.
Peel has long argued that Liverpool is a better choice for companies looking to ship goods to the north of the UK. But Mr Whitworth says it will take time for shipping lines to move services from existing routes to southern ports.
Mr Whitworth said: "We've never said on this day we will open. It's always been phased and very, very deliberate.
"We have therefore invested £400m on the basis of changing a market in the long-term, as opposed to one lightbulb moment."
After a sinkhole that opened up by Liverpool2 in February last year was repaired, the port has been building up its capacity and staff have been getting used to the operation of the terminal and the bigger container volumes coming through it.
Mr Whitworth said: "You and I might just see a box lifted off a ship and put down on the ground or onto a truck. But the arc of that movement, degree by degree, can make a big difference to productivity. So that's been evolving over the last year or so.
Maersk Line’s Colombia Express service, which serves New Jersey, has moved here - as has 2M’s TA2 transatlantic service, opening up direct links from Liverpool to the southern USA.
Last week a high volume of lorry drivers at the port combined with a power cut to cause long delays for hauliers at the port, with some drivers calling the Echo to complain.
But Mr Whitworth says those delays were resolved within hours and that ever since the port has been coping well with the added volumes. Peel also supplied more "comfort facilities" for drivers, including seating and extra toilets, while there were delays.
The ECHO was given a tour of the Liverpool2 terminal to see it in operation, with the automated cranes delivering containers to a steady stream of lorries flowing smoothly in and out of the port.
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Mr Whitworth said: "Within 48 hours, this port was delivering a service turnaround time of less than an hour, which is considerably below the norm in any event. That is better than average.
"The quayside operations were sweet as a nut. The thing that went wrong was just the volume of drivers they had to contend with and then the unexpected power supply outage. None of us could have anticipated that."
Delays were also caused because many of the drivers waiting on the bigger ships were not registered at Liverpool and had to be signed up. A side-effect of what Mr Whitworth called last week’s "perfect storm" is that more drivers than ever are now registered in Liverpool, making it easy for them to visit in future.
Meanwhile the port has done a deal with ADM for animal feed, making it that company’s biggest import facility in the UK. Port staff are also developing their vessel tracking systems, already the most advanced of their kind in the UK, while some 350 outsourced staff have been brought in-house with Peel as the company prepares to grow.
The port has also welcomed a new container rail service from Liverpool to Glasgow, which Mr Whitworth said had already been a success.
And now its boss is focusing again on attracting new ships to Liverpool.
He said: "I'm confident we will have some good news to share in the not too distant future."