The company said drivers are happy to pay more after saving money during lockdowns, and more workers are looking to drive to offices rather than take public transport.
In the six months to August 31, pre-tax profits hit £51.1m compared with just £3.9m in the same period a year earlier during the height of the pandemic. Revenues rose 71.9 per cent to £1.9bn.
As a result, full-year profits are likely to be more than £65m - above market expectations of between £50m and £55m.
But bosses warned that the supply constraints continue and cost pressures remain - particularly those related to staffing, which are set to increase by £12m.
The company said the extra cash for workers is to ensure employees do not leave at a time of high vacancy levels and wages going up across various sectors.
Growth was particularly strong in the used car market, with sales up 67.3 per cent. By comparison, new vehicles were up 44.8 per cent.
Vertu said: "The used vehicle market in the UK has experienced unprecedented market dynamics, resulting in record vehicle pricing levels.
"The reduced new and used vehicle market in lockdown, together with new vehicle production disruption due to Covid-19 and parts supply disruption (particularly semi-conductor shortages), has caused used vehicles to be in increasingly short supply.
"This tightness in supply has coincided with a period of strong customer demand for used vehicles.
"The reasons for this include increased savings levels by consumers during lockdown and the absence of alternative spending options (such as holidays), and also consumers wishing to avoid public transport.
"The benefits of the private motor car have been firmly re-established in the consumer's mind, which is much to the long-term benefit of the group."
New cars have struggled to roll off production lines due to the chip shortages, but Vertu said customers are "increasingly accepting of long lead times".
Its commercial fleet business also saw strong growth, with particularly high demand for vans.
Bosses said this was due to "lockdown savers" spending their cash on home improvements, leading to a rise in demand for tradespeople buying vans.
The company added: "In addition, the growth in online retail purchases has fuelled demand from delivery drivers. This demand has come at a time of limited supply, driving up prices and margins."
There was also strong demand for aftersales services, adding to the increase in profits.
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