A solution has been found to a steering fault affecting up to 400 taxis made by Coventry firm LTI, say administrators running the firm.
The fault led to the suspension of sales of the vehicles. Work to fix the problem is expected to take a month.
LTI's parent company Manganese Bronze went into administration this month.
Administrators PricewaterhouseCoopers (PwC) said there will now be a "rapid replacement" of the affected parts in the recalled vehicles.
PwC's Matthew Hammond said: "The company's employees will be part of a massive effort to begin fitting the new UK-supplied steering box to the recalled fleet within the next 48 hours."
'Take several weeks'
Jobs were lost at both the group's head office and manufacturing site in Coventry, with 99 out of 176 employees there being made redundant when the firm went into administration.
There were more job losses at dealerships in London, Manchester, Leeds, Edinburgh, Glasgow and Coventry, with 57 out of 98 employees facing redundancy.
The administrators said they will continue to work with the London Mayor, Transport for London, and the Licensed Taxi Drivers' Association.
"We are working to get taxis back on the road as quickly as possible but clearly, with the large number of vehicles affected in London and also in the regions, this work will take several weeks to complete," Mr Hammond said.
New unregistered taxis will also be fitted with the new components and put on the market in early 2013, the administrators said.