As a UK Citizen, you are eligible for the VWP (Visa Waiver Program).
Upon entering the US by land, all you'll need is your passport and to not have entered any of the few proscribed countries in the past. Look at this page on the CBP web site. I've quoted Point 4 below, but you'll probably want to read the whole thing and ensure none of the issues apply to you. If they don't, you'll be allowed to stay in the US for up to 90 days, no problem.
4. What are the specific changes to the VWP?
Under the Act, travelers in the following categories are no longer eligible to travel or be admitted to the United States under the VWP:
- Nationals of VWP countries who have traveled to or been present in Iran, Iraq, Sudan, or Syria on or after March 1, 2011 (with limited exceptions).
- Nationals of VWP countries who are also nationals of Iran, Iraq, Sudan, or Syria.
These restrictions do not apply to VWP travelers whose presence in Iraq, Syria, Iran, or Sudan was to perform military service in the armed forces of a program country, or in order to carry out official duties as a full-time employee of the government of a program country. These military and official government services exceptions, however, do not apply to the dual national restriction.
Travelers who are known to fall into the dual national category noted above will receive notice via email on or about January 21, 2016 that their current ESTA is no longer valid.
The Act also requires that all VWP travelers use an electronic passport for travel to the United States by April 1, 2016. Finally, the Act includes other changes to the VWP to promote enhanced information sharing of terrorism and criminal data, and use of INTERPOL databases and notices for border screening purposes.
The vast majority of VWP eligible travelers will not be affected by the legislation.
Finally, this answer has only been about entering the US. To fly into Canada, as commented by @Michael Hampton, you will most likely be eligible for and want to apply to receive an eTA (Electronic Travel Authorization).