Sports Minister Richard Caborn has ruled out any chance of the government giving more money to Silverstone. The circuit is not on the provisional Formula One calendar for 2005, with its owners unable to meet Bernie Ecclestone's price for hosting a race.
But Caborn says the government will not be making up the shortfall.
"Is it right that a cash-rich, asset-rich sport should take money out of (the government's overall) sport budget?" he said to Five Live.
But the Motor Sports Association, which governs British motorsport, believes the repercussions will reverberate well beyond Formula One if the British Grand Prix is dropped.
Its chairman John Grant said: "It is widely acknowledged that the British Grand Prix makes a significant and direct contribution to the UK economy each year and that it is an important flagship for the hugely successful British motor sports industry.
"We seem to have arrived in the situation where a funding shortfall of some �2m to �3m a year is standing in the way of retaining an iconic event which is vital for our sport.
"It directly contributes some �40m a year to the local economy and the government's tax revenues, and is needed to sustain the prestige of an industry that is responsible for international trade worth in excess of �3bn annually."
His words were echoed by ex-Sports Minister Kate Hoey, who called on the government to help Silverstone.
"It's not just about sport, it's actually about the future of the motor industry in this country," she told Five Live.
"It seems to me that they haven't actually thought through the repercussions of losing it. "What message does this send to the world and to our competitors in terms of an Olympic bid?
"I do think that while we hope Bernie Ecclestone is playing hardball and that something may get sorted out, we can't go on year after year having this (Silverstone debate).
"This government has to decide whether it cares about the whole industry to actually put some tangible support into it."
The Department of Culture, Media and Sport said in a statement on Thursday: "The government has already made significant financial contribution to motorsport and to Silverstone.
"In 2002, we invested over �16m to support the industry and �8m to improve road access around the track.
 | If you lose the history of F1, that could be damaging to the long-term future of F1  |
"Clearly the government supports and wants to see a British Grand Prix at Silverstone but the current commercial negotiations about the promotion of the GP are a matter between the British Racing Drivers Club and Formula One."
Former world champion Damon Hill is not surprised the British GP has been axed.
"It's not unusual, Formula One is always putting the squeeze on promoters and everyone," Hill told Five Live.
"It's just economics. F1 has made no qualms about moving on from great teams like Lotus. You can't keep on propping things up if they're making no money.
But he added: "If you lose the history of F1, that could be damaging to the long-term future of F1."
Hill, who won the world championship in 1996, believes there is a chance the British GP could be saved but believes Eccleston favours London over Silverstone.
"This sort of thing has happened before and it could be just a negotiating tactic," he said.
"But Bernie Ecclestone is serious. He doesn't believe Silverstone is up to it.
"Given the choice, I think Bernie would prefer it to be in London."