The lawsuit names three UK ministers, David Miliband, foreign minister, John Hutton, defence minister and Peter Mandelson, business minister.
Speaking to Al Jazeera, Phil Shiner, a UK lawyer who represents Al-Haq in Britain, said: "International law is very clear on this issue.
"All states are under an obligation not to render assistance and not to recognise the illegal situation [in Gaza] and to co-operate together by all lawful means to end that particular situation ... and to ensure respect for the Geneva Conventions.
"The UK government has gone completely in the wrong direction. It has increased its arms exports [to Israel]. It continues to import Israeli arms, it continues to invite Israeli arms manufacturers to arms fairs here".
In pursuing the lawsuit, Shiner said "all that's in our way is that obviously it's a controversial topic. Judges might be frightened of entering this territory but once they do the law is very clear".
Last month, Amnesty International, the UK-based human rights organisation, called on the British government to suspend all military exports to Israel until there is no longer a substantial risk that such equipment will be used for serious violations of human rights.