The Conservative deputy, who campaigned for a Leave vote in the EU referendum, spoke out after UK Chancellor Philip Hammond said the treasury would guarantee to back EU-funded projects signed before this year's Autumn Statement.
The UK government also gave an assurance that agricultural funding now provided by the EU will also continue until 2020.
Bashir, Conservative spokesperson on small businesses, said: "The announcement shows that the alarmism of Project Fear was unjustified. Far from the chaos predicted by the scaremongers, this announcement brings continuity and stability."
He added, "Far from cutting off funding, leaving the EU means we decide ourselves as a nation what we do with our own money. It vindicates our decision to take back control.
"The cost is put at €5.2bn - but that is a fraction of the €17.4bn we have been sending Brussels every year."
Meanwhile, the German Green party says Angela Merkel's government should offer fast-track citizenship to UK people living in Germany.
The opposition party has written to Merkel's government calling for a reduction in the length of time a candidate should have lived in Germany before being eligible for citizenship.
Current guidelines are for eight years, reduced to six for someone who has made a special contribution to German society and to three for those married to Germans.
The government has suggested decisions be made on a case-by-case basis at the discretion of Germany's 16 states.
The news comes after it emerged that the authorities in Brussels have seen a mini surge of applications for Belgian nationality from British expats living and working in the city since the vote.
In one commune, Ixelles, applications have risen 10-fold since the vote.
Meanwhile, the UK's relationship is likely to "remain strong" with EU countries, especially with large numbers of British expats contributing to their local economies, according to the Fry Group, which offers tax and financial planning for expatriates.
With the full repercussions from the EU referendum only now starting to be felt, a spokesperson said, "Brexit or no Brexit, British people will continue to be able to buy property in European countries and live in them, just like nationals from non-EU European countries have done for decades, even centuries."
The group, which has offices in various cities, including Brussels, predicts that Brexit could take various formats.
One is that the UK remains in the single market with Britons keeping their right to live and work in the EU, similar to citizens from Switzerland, Iceland and Norway.
Another is that the UK leaves the single market but negotiates terms individually with EU countries, such as Spain, where Britons' rights remain essentially unchanged.
A third option, it says, would see the UK leave the single market and Britons left with similar rights to buy property in or move within the single market as do other non-European nationals such as Australians and Americans.
The various scenarios are mapped out in a policy paper.
A spokesperson said, "The news that the UK had voted to leave the EU had a major effect on the value of sterling against other world currencies, weakening it significantly against its major pairings of the euro and US dollar.
"Even the welcome news about better than expected economic growth prior to the referendum could not have much of a positive impact on sterling's strength. Markets are still unsettled by the medium and long-term uncertainties in the UK, leaving sterling likely to continue fluctuating."