The Conservative MP for New Forest West said: "Will he summon Forestry England and threaten them with the rough end of a pineapple and instruct them to use their position on the board and their substantial shareholding to get those campsites open?"
Mr Sunak replied: "I'm not sure I have the power to summon anyone but I will be delighted to bring whatever influence I can to bear on his particular matter and look forward to discussing it with him further."
Last month Camping in the Forest announced it was still not viable to reopen its 16 sites across the UK from a "safety, operational and financial perspective", despite sites being allowed to reopen after coronavirus restrictions were eased.
Visitors occupying the 3,100 pitches contribute more than than £16m to the New Forest economy during a summer, according to New Forest District Council estimates.
Sailors from Royal Navy aircraft carrier HMS Prince of Wales are helping to run Covid-19 testing stations.
The teams from the Portsmouth-based warship are currently manning seven mobile testing unit sites across Hampshire including Eastleigh, Fawley and Brockenhurst with further assistance planned for Farnborough and Alton.
The crew members are carrying out the work while the Prince of Wales is undergoing maintenance ahead of sea trials including embarking F-35 Lightning jets for the first time.
Nearly 3,000 military personnel are involved in assisting with the national response to the pandemic, with Royal Marines also running testing centres in the South West.
The coronavirus, which causes the respiratory disease known as Covid-19, was first confirmed in the UK at the end of January.
Data as of Monday 6 July.
Libraries reopen across Dorset and Hampshire
Libraries across Dorset and Hampshire are reopening this week as coronavirus lockdown restrictions continue to ease.
Local authorities throughout the area have confirmed the facilities will open with new socially-distanced layouts and other safety restrictions.
These include Hampshire County Council asking library users to limit their visits to a maximum of 30 minutes.
In Bournemouth, Christchurch and Poole the local authority has announced phased openings beginning on Monday morning.
Worshippers take in church service from their cars
Worshippers stayed in their cars as a church held its first drive-in service in Hampshire.
St Barnabas Church in Swanmore held the special service which meant parishioners were able to sing for the first time since the start of the lockdown.
Despite the the relaxing of measures, people attending religious services are still not allowed to sing inside.
The Rev Claire Towns, who conducted the service, said: "I think people have loved it - just the novelty of it and actually being able to sing with other people around them. It was just a great thing to do."
She said it was possible the services could be held on a monthly basis in Swanmore Village Hall's car park - but she had conducted her first full service with worshippers back inside the church earlier.
The communion service was held at 08:00 BST but only 19 people could attend.
Towns said: "It was great to be able to do that and look out on people in pews as opposed to empty pews, like the last few months.
"But it wasn't the same and if they're the kind of numbers we're going to be accommodating from now on...without any singing that has a massive impact on the feel of worship."
Coronavirus: Cases confirmed in Hampshire and the Isle of Wight
number of cases of Covid-19 has been confirmed as 6,399 in
Hampshire and 421 on the Isle
The total is up by two cases
in Hampshire since Thursday. It has stayed the same on the Isle of Wight since then.
The breakdown of the figures by local authority area is: