The automotive industry and Airbus have offered tentative support to Theresa May’s proposed Brexit deal, warning that the “cliff-edge” no-deal alternative would be much worse for the UK.

Backing from representatives of an industry and a company that collectively support nearly a million jobs in the UK will boost the prime minister’s hopes of securing parliamentary approval for her plan before the 11 December vote.

Airbus, which directly employs 14,000 people in the UK, has previously warned it would be forced to reconsider its investment in Britain in the event of withdrawal without an agreement, a scenario the aerospace giant described as “catastrophic”.

But Katherine Bennett, the UK head of Airbus, told MPs on the business select committee that May’s deal would allow the company to emerge from a “holding pattern”, during which it had not rubber-stamped new investment in the UK.

“If the withdrawal agreement is successful in some form or another then Airbus would consider continuing to invest as the company has done over many years,” she said.

“We have great capability, but obviously because of the uncertainty, which we want to see reversed, that is why investments have been put on hold.”

Paul Everitt, the chief executive of the aerospace and defence trade body ADS, said Airbus was not the only firm to have frozen investment in the UK due to uncertainty about the future EU relationship.

However, the pharmaceutical industry sounded the alarm on the logistics of securing the supply of ingredients for more than 12,000 medicines made in the UK after Brexit, and warned that higher costs would eventually translate into higher drug prices.

Appearing before the business committee at a separate hearing, Mike Thompson, cthe hief executive of the Association of the British Pharmaceutical Industry (ABPI), said drugmakers were working with the government on how to secure the supply of ingredients from abroad.

He described it as the “biggest logistical challenge that we’ve ever faced”, adding: “There will be unknown consequences where things don’t go right and those are the sort of things that are keeping us awake at night.” He stressed that the number one priority for the industry was a transition period.

Thompson also said the ABPI’s members had stockpiled an extra six-week supply of drugs, as instructed by the government.

The Society of Motor Manufacturers and Traders (SMMT), the trade body for a sector that supports 800,000 jobs, also backed the prime minister.

At the SMMT’s annual dinner on Tuesday night, its chief executive, Mike Hawes, said there was “no Brexit dividend” for the automotive industry, which has consistently lobbied for the UK to stay in both the customs union and the single market.

“Leaving without a deal would be catastrophic – plants will close; jobs will be lost.”