Baradar was released from jail in Pakistan as part of efforts to kickstart Afghanistan's peace process, but he has since been kept under house arrest, reportedly in Karachi or Peshawar, to the fury of Afghanistan.
"We will look for explanations from the Pakistan government for the exact whereabouts of Mullah Baradar and how can Pakistan facilitate direct talks between Mullah Baradar and the High Peace Council," Karzai's spokesman Aimal Faizi told AFP.
Afghan officials believe that Baradar, who had been held in jail in Pakistan since 2010, could encourage Taliban leaders to seek a negotiated settlement to end the 12-year insurgency if he were fully at liberty.
About 400 Afghan soldiers or policemen die every month fighting the Islamist militants.
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"Prime Minister Nawaz Sharif promised the release of Mullah Baradar, which they did, but Mullah Baradar is still under very strict supervision by Pakistan authorities," Faizi said.
Apparent headway between then-Pakistani president Asif Ali Zardari and Karzai at the last summit hosted by Cameron in February quickly unravelled in a series of public rows.
"There have been ups and downs in the past but that should not stop us from working with Pakistan," Faizi said late Saturday.
"The focus of the meeting will be Pakistan support for the Afghan peace process, fighting terrorism and extremism, and Pakistan support for the security of the Afghan 2014 election."
"Pakistan can play a role to maintain Afghanistan security for upcoming elections because these terrorists are coming from the other side of the Durrand Line (border) to Afghanistan," Faizi said.
Karzai, who must step down next year after serving two terms, will also give a speech at the World Islamic Economic Forum in London, and at the Oxford Union, the university's debating society, during his four-day visit.
The search for a peace deal in Afghanistan is urgent as 87,000 NATO combat troops prepare to withdraw next year and the national army and police take on the fight against insurgents.