President Vladimir Putin and Prime Minister Gordon Brown have not had a single conversation since Putin rang to congratulate the premier on taking office on June 27 last year, the British tabloid said.
The paper cited diplomats as saying Russian attempts to establish contact had been "blocked by a stubborn Downing Street."
Putin will cede the presidency to First Deputy Prime Minister Dmitry Medvedev on May 7, and is likely to become prime minister. Under Russia's current setup the president has far greater powers than the premier, but Putin is widely expected to assume a commanding role in his new job.
"Brown should have spoken to Putin. The real power will remain with Putin and there can be no repair in relations between our countries without the main man being involved," a Russian diplomat was quoted by the paper as saying.
"The current silence is the worst since the Soviet old guard of Brezhnev, Andropov and Chernenko were in the Kremlin."
Relations between Britain and Russia have been strained by the diplomatic fallout following the murder of Russian security service defector Alexander Litvinenko in November 2006 in London, and more recently by the closure of British Council offices in Russia.
Gordon Brown is subjected to regular criticism in the British media over his apparent lack of diplomatic skills and his stubborn personality. Last year Lord Turnbull, a former civil service chief, famously accused the then chancellor of treating his colleagues with "Stalinist ruthlessness."
Former Prime Minister Tony Blair held regular conversations with Putin, with whom he was reportedly on first-name terms.
A British diplomat told the Daily Mail: "Part of the problem is that Brown does not have Blair's charm or his ability to defuse difficult situations. Also, he is not particularly interested in foreign affairs, or at least not the traditional power balances."