As the Conservative party conference starts, the Brexiteers have drawn up the battle lines between the prime minister’s “deranged” Chequers deal and what they claim is a “better” alternative for leaving the EU.

The rightwing thinktank the Institute of Economic Affairs (IEA) accused Theresa May of “approaching Brexit from the wrong end” when it launched its Brexit blueprint earlier this week. “I think the prize is in the independent trade policy,” said its author, Shanker Singham. Even the international trade secretary, Liam Fox, now admits that independent trade deals will not be as easy as previously enthused.

The IEA’s plan would give the UK a “basic” free trade agreement for goods, while allowing the UK government to simultaneously discuss long-term free trade deals with countries including the US, China and India. On the question of the Irish border, Singham said the IEA’s proposal was designed to “avoid a hard border in the island of Ireland”. This would involve a range of elements, he claimed, “including the use of technology”. Basically, this would see the UK accepting a Canada-style deal.

Then up pops Boris Johnson with his “super-Canada plan”, also insisting his vision would also not lead to a hard Irish border. This super-Canada deal would mean:

• zero tariffs and zero quotas on all imports and exports

• mutual recognition agreements covering UK and EU regulations to ensure “conformity of goods with each other’s standards”

• technological solutions to keep supply chains operating smoothly

• a deal covering goods as well as services.

It all sounds so easy, but it’s not. All these plans are being discussed as plausible, yet time is alarmingly running out. There is grave concern that an agreement will not be reached at the EU summit next month. And the EU has suggested the latest a deal could be finalised is November – that’s just eight weeks away.

The Canadians have a trade deal with the EU called the comprehensive economic and trade agreement (Ceta). There are five reasons why this isn’t a viable roadmap for Brexit.

1. Ceta is a trade agreement, not a customs union

Under Ceta the EU checks products coming from Canada to ensure they do not originate in any other country – because if they did, they would be subject to EU tariffs. The same would happen if the UK had a Canada-style deal with the EU. Products exported from the UK to the EU would need to be subject to EU customs controls so the EU could ensure they were not originally from other countries that did not have free trade agreements with the EU – in effect, to prevent attempts to use the UK as a backdoor to avoid tariffs. These customs controls would probably mean delays at the UK/EU border, causing problems for UK manufacturers.

Technology does not yet exist to alleviate the problem. As the manufacturers’ organisation the EEF has said, a Canada-style deal would require billions to be spent on new technology and infrastructure in the UK and the continent, which would take years to implement. “As a result, it would put thousands of manufacturing jobs and hundreds of billions of pounds of exports at risk and, at worst, could destroy much of Britain’s manufacturing base,” said the EEF’s chief executive, Stephen Phipson.

2. No common rule book exists between the EU and Canada

Canada sells 76% of it products to the US. Because of this, many Canadian standards are similar to or the same as the US’s but different from the EU’s. If Canadian companies want to sell products to the EU, they have to prove those products conform with EU product safety, health and environmental rules. This involves extra bureaucracy, controls and paperwork. If the UK had a Canada-style deal with the EU, UK companies would have to do the same. This would mean no frictionless trade between the UK and the EU. Also, UK companies exporting to the EU would have to comply with EU rules without having any say in setting them.

3. A Canada-style agreement would mean a hard border with Northern Ireland

Border controls would be required between the UK and EU to check compliance – including between Northern Ireland and the Republic of Ireland. This would be a violation of the Good Friday agreement – and would disrupt two decades of hard-won peace on the island of Ireland.

4. Ceta does not cover services

The UK is a 80% service economy, comprising arts, entertainment, recreation, transport, storage, IT, finance, insurance, professional, scientific and technical services. So a Canada-style deal that covers goods alone would not solve the problems of Brexit. Ceta also does not cover passporting of financial services. Passporting allows UK-based financial services providers to provide services to customers in other EU countries, as long as they are licensed to do so by a UK regulator. This would not be possible under a Canada-style deal, and would have a significant impact on one of the UK’s largest export sectors.

5. Ceta does not allow the free movement of people

From teaching, the NHS and social care, to cleaning and building, the UK economy depends heavily on EU workers. Under a Canada-style deal for the UK/EU, the ability for EU workers to live and work freely in the UK would stop. Allowing only skilled workers from the EU into the UK will not resolve this issue.

So I would implore Conservative MPs to start talking facts not fiction, stop the peacocking and think of the people of the UK and the human cost of the various Brexit plans they have. Cutting through the bluster and noise, there appears to me only one real choice. If the UK wants to leave the EU, we need to stay in the single market. If the politicians come to their senses and realise this too, then they must let the people of Britain decide if this is what they want or if they want to remain in the EU, fight for reform from within, and keep a deal which has kept Britain prosperous and peaceful.

• Gina Miller is a transparency campaigner and founder of End the Chaos