The sale will produce a third force in the car leasing business, with 40,000 vehicles in the combined fleet compared with 50,000 at Lex and 60,000 at Cowie.
It also marks another stage in TSB's divestment of its non-core businesses, which has already included the sale of Swan National Motors, the car retailer, for pounds 46m.
The bank still owns Swan National Rentals, a car hire firm, but this is also for sale at the right price, as is the merchant banking subsidiary Hill Samuel. But last week the bank revealed that it had failed to sell its estate agency chain.
TSB's profits for the year to September will be boosted by about pounds 20m on the new accounting basis.
The payment will be pounds 57.9m in cash for the company's net assets and pounds 124.6m to repay inter-company debt.
Analysts said the sale price was a good one for a company with pounds 7.3m profit before tax and head office costs of pounds 700,000 last year. Net assets, excluding subordinated debt, were pounds 27.1m.
There are understood to have been a number of other approaches for the company, which employs 300 people compared with 80 at Forward Trust's vehicle leasing subsidiary, Crown Vehicle Contracts.
Graham Picken, Forward Trust's chief executive, said he believed the price was reasonable for a business that made pounds 7.3m. Many companies that had deferred replacing their old cars were finding their costs rising and deciding to change them at last.
He added: 'We think the market is improving. It is patchy, but the economy is on the right track. We think we can grow the business over the next few years.'
Vehicle leasing is one of a number of specialist financing businesses owned by Forward Trust, whose ultimate owner is the HSBC banking group. It includes instalment credit, leasing, factoring and unsecured personal loans.
Mr Picken said a few jobs would be lost at Crown, which is based in Bristol, but others would be created at Swan.Reuse content