The Glasgow-based company has started preparing for a move south of the Border after recording strong sales at the store the company opened in its home city to sell products from scooters to walking sticks.
"The big store is going terrific," said Gerry Facenna, who founded Allied with his brother.
Mr Facenna said Allied Vehicles was looking for suitable sites in England and expected to open a mobility store in the country within nine to 12 months.
Mr Facenna believes the store's operation will allow Allied Vehicles to capitalise on increasing demand for products that can improve people's mobility as the UK's population ages.
He expects the retailing operation will help Allied Vehicles maintain strong growth following a year in which the company grew profits by a third.
The company's latest accounts show Allied made pre-tax profit of £1 million in the year to April compared with £743,000 in the preceding period.Sales rose 11%, to £73.3m from £65.7m.
In the accounts directors wrote: "Allied Vehicles continues to lead the market in wheelchair accessible vehicle (WAV) and taxi design build and sales. During the year we increased our share of the motability market to 38%."
Mr Facenna said recently that he believed some taxi drivers who deferred buying vehicles during the long economic slowdown had returned to the market.
The company may be entering a crucial phase in its long-running attempt to get the taxis it produces in its sprawling Possilpark plant approved for use in London. Representatives are due to meet officials from the London Public Carriage Office next month. The office requires taxis to turn in a 25-foot circle.
"We could create 100 jobs if we could get it passed," said Mr Facenna. The firm has said it may consider taking legal action if the authority does not relent.
Allied Vehicles received a strong boost to trading during the year to April when it won a three-year contract to supply wheelchair accessible and adapted vehicles on rental across the UK under the Motability scheme. Directors wrote the company had been required to add 95 vehicles to its rental fleet. It had 125 accessible hire vehicles in April.
Mr Facenna is campaigning for a £1m scheme to use taxis as ambulances in a bid to boost survival rates among heart-attack victims.
The motor trade veteran has said he made a good recovery from a heart attack he suffered 18 years ago.
Allied Vehicles employed a monthly average of 370 people in the year to April, compared with 344 in the preceding year.
Mr Facenna said it had recruited 100 people since January.