The UK cabinet office has rejected a £33m proposal to double the capacity for French government passport checks at the port of Dover, raising the prospect of long delays for passengers after the end of the Brexit transition period.

The English Channel port, which handles 2.2m passenger vehicles every year, had requested the funding as part of the £200m Port Infrastructure Fund announced by the government in October to pay for additional border facilities required as a result of the UK’s departure from the EU.

According to a person familiar with the matter, Dover applied for £33m to double the number of French government passport booths from five to 10 in anticipation of more stringent requirements including stamps in passports after January 1.

The application was rejected, however, with Dover receiving just £33,000 for an unrelated project, according to a list of the PIF awards seen by the Financial Times.

Dover has repeatedly warned that it will need to substantially boost capacity for French controls, which under a reciprocal bilateral agreement enables passports to be checked before boarding the train or ferry to France in order to ease traffic flows.

A National Audit Office report released last month said the government’s reasonable worst-case scenario was that passenger queues could last one to two hours after January 1, but warned that in the summer “the queues and delays could become much longer”.

Tim Reardon, the head of EU exit at Dover, echoed those warnings in evidence to the House of Lords’ EU select committee last month, saying that French controls would become “more intrusive, and therefore slower” after January 1.

“That means we need more French kiosks in order to maintain the rate of flow,” he added, confirming that Dover had applied to the Port Infrastructure Fund and was “hopeful” of a positive response.

However, Dover was disappointed when the results of the fund’s bidding process were detailed in a letter to affected MPs ahead of an expected public announcement on Wednesday.

France is deploying 700 extra customs officers and veterinary inspectors to its Channel ports, including the entrance to the Channel Tunnel near Calais, and has spent €40m on a new IT system and handling facilities. New parking zones have been paved and set aside for trucks without the correct paperwork.

French government agencies have also conducted test runs of the control systems that will be in place at the borders regardless of whether the UK and EU reach agreement on their future trading relationship before the end of the post-Brexit transition period. One official in Paris with knowledge of the customs plans this week expressed surprise at the “mess” and apparent lack of preparations for January 1 on the English side of the Channel.

In its letter, the cabinet office explained that the PIF had been more than twice oversubscribed, receiving 53 applications totalling £450m.

After discounting ineligible bids, such as those deemed to be supporting the development of “wider commercial opportunities”, and forcing reductions on some other applications, the fund allocated £194m to 41 ports across the UK.

Among the big winners were the east coast ports, including Harwich which received £22.9m, and the Humber ports of Hull, Immingham and Killingholme, which received a total of almost £56m.

However, the government said that the oversubscription to the fund had required it to finance only 66 per cent of the value of successful projects — leaving even some successful bidders disappointed.

Those warning of being underfunded included Portsmouth, which received £17.1m — a figure which the city’s Labour MP Stephen Morgan said still fell “far short” of what was required.

“The funding awarded is not enough to cover the major infrastructure work mandated by the government’s own border operating model, and without additional contingency funding it cannot be completed in time,” he said.

Port of Dover and the cabinet office did not immediately reply to a request for comment.