HTML search box

I'm trying to find out if there's a way to add an HTML search box to my website that will open up the page searched for?

Example: I have the search box on the homepage. I have pages, each with the name of a British city. If a visitor using the search box searches for "London" they will be taken directly to mysite.co.uk/london.

I can't find a search box code anywhere that will allow me to do this. Is it even possible?