In contrast, the US government has frozen $30bn (£18bn) of Gaddafi family, LIA and central bank assets.
The European Union has frozen assets of Col Gaddafi and five family members.
It has also banned the supply of arms, ammunition and any equipment that could be used for "internal repression".
Austria has also confirmed it has frozen assets belonging to the Gaddafi family. The country's central bank said about 1.2bn euros ($1.7bn; £850m) of Libyan assets were currently held in Austrian accounts.
Germany said it had blocked an account holding 2m euros held by one of Colonel Gaddafi's sons.
The UK Treasury has not confirmed the value of the Gaddafi family assets that it has frozen, but reports suggest a figure of £1bn.
End Quote Pepe Egger Exclusive AnalysisUntil very recently, it was very clear who was in charge of the [LIA's] money”
The UK has also stopped the export of about £900m worth of new Libyan dinars ordered by state authorities.'Uncomfortable' Pearson announced last summer that the LIA had taken a significant stake in the publisher, which owns the Financial Times and Penguin.
It said it had "reasonable cause" to believe the fund had since added to its holding.
Pearson chief executive Marjorie Scardino said she was "uncomfortable" with the LIA's shareholding.
The fund holds stakes in a number of other institutions, including Italy's Unicredit bank and industrial group Finmeccanica, as well as Canadian oil exploration group Verenex.
Reports also suggest it holds shares in Russian aluminium giant Rusal.
The fund, established in 2006, holds $70bn of assets and is the 13th largest sovereign wealth fund in the world, according to the Sovereign Wealth Fund Institute.
The fund, built on Libya's oil wealth, scores two out of 10 on the institute's transparency ranking.
'Paralyse' Governments across the world are deciding whether the assets of the LIA should be considered assets of the Gaddafi family and should be frozen, said Pepe Egger, head of western Europe forecasting at Exclusive Analysis.
If instead they are considered assets of the Libyan people, governments may feel they should not be frozen, Mr Egger told BBC News.
The question is particularly difficult in Italy, he said, given the extent of not just the LIA's investments in the country, but also those of the country's central bank.
"For example, the governor of the Libyan Central Bank is on the board of Unicredit."
If the fund's assets are frozen, then "it's shareholding rights will be put on hold. This could paralyse big companies," Mr Egger explained.
Together, both the LIA and central bank own more than 7% of Unicredit, one of Italy's biggest banks.
Such large shareholdings could be clouding what would otherwise be a fairly straightforward issue, he suggested.
"Until very recently, it was very clear who was in charge of the [LIA's] money," said Mr Egger.
"Libya was Gaddafi and Gaddafi was Libya."