Tamsin Allen said on Tuesday that her firm, Bindman and Partners, would "start the process" this week of seizing some Britain-based Saudi state assets, which include Saudi Arabian Airlines.
Her clients, Sandy Mitchell, Les Walker and William Sampson, who is British-Canadian, won a landmark case last October in which Britain's appeals court effectively removed blanket immunity for officials from foreign states accused of serious crimes like torture.
The men were held in Saudi jails for more than two years and confessed, allegedly after torture, to plotting a series of bomb attacks in Riyadh in 2000 and 2001.
Riyadh authorities described the bombings, in which one Briton was killed, as part of a turf war between Western gangs supplying illegal liquor to expatriates in the state, but critics reject the argument as a way to scapegoat foreigners instead of local fighters.
The appeal court ruled that the men, along with a fourth Briton jailed by the Saudis, could sue individuals, including their interrogators and Saudi Interior Minister Prince Naif bin Abdul Aziz.
"The news is that they're not paying the costs. And we're going to therefore seize an asset"
Bindman and Partners law firm
It threw out the Saudi demand for blanket immunity, and ordered Riyadh to pay for the legal costs of its appeal to that decision, believed to be more than 100,000 pounds ($180,000).
Allen said that although the Saudis had not contested the legal costs, they had failed to pay, and would now face the "normal" procedure of having assets seized.
"The news is that they're not paying the costs. And we're going to therefore seize an asset," Allen said. "They may try to stop us and they may succeed in stopping us, but they haven't done that yet."
The lawyer said the Saudi state was trying to take the matter to Britain's highest court of appeal, the Law Lords, while its refusal to pay had forced her clients to use public legal aid funds.
"We, our clients and the public funding authorities are all outraged that Saudi Arabia, one of the richest states in the world, should force the hard-pressed legal aid fund to pay its debts and at the same time use our courts to seek immunity from torture claims," she said.
The Britons' compensation claim will only be able to move forward once the Saudi appeal is either rejected or dealt with by the Law Lords, she said, adding that settling the issue of immunity would "open up the way for straightforward claim for damages for torture".