You can do this... but I don't think you want to.
You absolutely cannot drive in Canada without automobile insurance, so that means you're going to have to get all your documents in order to apply for Canadian automobile insurance. Since presumably you have no insurance coverage now, you are going to have a real devil of a time finding an insurer that is prepared to put in an hour or two of underwriting effort to write a policy that you are going to cancel less than a month later. Note also that there will be minimum retained premiums on such policies, meaning that what you pay for a short period of time will be disproportionately large.
The other complication is that once you get to the US, you're going to have to import that Canadian car, and that's complicated unless you buy an older vehicle. It'll have a speedometer in km/h and an odometer in km, which means it will be more difficult to sell when you're done with it (unless you re-export it back to Canada) and you will get less money for it. It will also likely have to pass a safety inspection in your new US state, whereas a vehicle bought locally there may not, or may be subject to a less stringent inspection. You're also going to have to buy US insurance on it, and now you're going to have to provide evidence not only of your UK history but also your Canadian history, including the policy you bought in Canada just a month ago. It's going to be a lot of work.
Also, it is up to the state(s) through which you will be passing if they will accept your temporary Ontario registration. They probably will, but if you get stopped by the police, it could be extra hassle providing evidence that you have a valid registration. Unlike in Ontario, the police in the US will not be at all familiar with temporary Ontario registrations. The vast majority of US police officers will never have seen one.
My advice: if you're crossing at a border crossing that is near cities on both sides of the border, rent a vehicle in Canada, cross the border with it, rent another vehicle on the US side, transfer your belongings, and then drive the Canadian vehicle back to Canada to a nearby rental office, and get a ride back across the border. Alternatively, many rental companies will do one-way rentals across the border, but it may be at an extra fee. If you're lucky, the rental agency will have US vehicles they want to get back in the US. If you're hiring a truck (e.g. U-Haul), crossing the border should be zero problem as I find many of the Canadian U-Haul vehicles have US registrations already.
Late edit: Additional point: unless you have the vehicle registered for sufficiently long in Ontario, you are going to have to pay Ontario HST (harmonized sales tax) on it when you register it, and then pay tax in the US state in which you settle (assuming things work similarly there to here). Where I live (Saskatchewan) you need to have had a vehicle registered for 30 days minimum in your prior state/province in order to not have to pay Saskatchewan sales tax when you import it here.