We are looking for an automation tool which can be helpful in doing single user performance testing for a Web Application based on UI i.e. recording how many seconds it takes to load the entire page. Is there one? If yes, which one is most popular?
Any data available on the Chrome Developer tools can be retrieved automated with their API: https://chromedevtools.github.io/devtools-protocol/
Try https://www.webpagetest.org/ This is perfect tool for testing performance of UI.
recording how many seconds it takes to load the entire page
There are online services like https://www.webpagetest.org/ or https://tools.pingdom.com/ - these tools measure the overall page load time, and the load time for the each element on the DOM level. Powerful, but the very technical results can be complicated to interpret. You can automate testing on such a website using Selenium ;)
Google developer tools (as mentioned by others above) give you the same result as webpagetest.org, but tested locally in your browser.
If you need timings on the user interface (not DOM) level (overall page load time, time for a certain AJAX-y action to complete, time for a certain image to appear or vanish...) then look at measuring the runtime with visual tools like Sikuli or Kantu for Chromium. You find the timings for each step inside the log file.