Could americans travel to england in the early 1800s? I am writing a screenplay for school and want to make it accurate.?

By ships.  That was known as the late Age of Sail.  Pocahontas lived the last part of her life in England and she traveled by ship. She died in 1617.  200 years later, ships were far-advanced, and the travel was much easier and more pleasant for those with money. 

The war pf 1812 was brought about in large part because of the British Navy taking US merchant ships as prizes, under the notion that they were doing trade with Britain's enemy, France, while Britain was at war with Napoleon.  In fact, outside of the US, where the war is a huge deal to Americans, that war is seen as a fairly minor engagement in the Napoleonic wars.

There were no commercial passenger ships, no boats dedicated solely to cruising.  Passengers traveled on merchant vessels as there was room for them and travelers often waited weeks, sometimes months, for there to be sufficient cargo for a trip to make financial sense.

Therefore, passengers were free to travel from the US to England, or anywhere a ship could take them.  They did so at their own risk.  Male passengers ran a serious risk of being impressed - taken by the British and forced to man British ships.

So you will want to research the state of sea travel during the period to make the plot believable. It would have been very, very dangerous and not very likely, but not impossible. Someone wealthy enough, like an American merchant who dealt in items sorely needed by British merchants, could conceivably strike a deal to have a certain voyage bound for England be off-limits to ships of the US Navy. Naval ships of the time communicated at sea by the flying of various flags that sent specific messages, and they also used private signals. Do some research.

But you WILL have to make a change to this girl's reason for going to England. It could not be to attend Oxford, or any university in England.  This did not begin until the Victorian era.  Your events take place during the late Georgian era, which was a time where women's education actually took a step backward. Literacy in women was still increasing, but the mindset of 'separate spheres' for men and women had firmly taken hold.  Women of means were taught by governesses or at 'dame schools', and they were taught to be in charge of the home. Men ruled the world outside of the home, so the traditional classic education was pointless for women.  The US was more progressive than the UK when it came to education for women, and there were plenty of places for wealthy families in the US to send their daughters to for 'finishing' - they wouldn't need to send them to a 'dame school' in England, and certainly not during a war.

You will need another reason to send this girl to England during this time.

Why is your heroine being sent to Oxford? if you are thinking of the University of Oxford, don't, unless she is going to be disguised as a boy.

Of course Americans traveled to Britain in the early 1800s.  Both Franklin and Jefferson had been there even earlier as US representatives.  BUT no women were admitted to Oxford, Cambridge, etc until the 1870s, and then without being able to get a degree!

I don't believe Oxford allowed female students before about 1875 or so. 

Travel was only possible by sailing ship.  When you say 'go to school' do you mean go to university?  Women were not allowed to attend Oxford University until 1920.  I hope that you don't have to film this screenplay because it will be very complicated.

Do some research. Google women in college and the year. I seriously doubt any woman was allowed to go to college back then.

Yes, there was shipping between America and England, but a young girl would not be going to school in the early 1800s.

You are aware that the British were able to travel to the United States since the 1600s with the mayflower so why wouldn’t the opposite be true. 

Haven't you ever read Little Women? Wealthy Americans frequently did something called the "The Grand Tour" of Europe. They traveled by ship, took huge trunks of clothing, and spent months touring the major highlights of England, France, Italy, and Germany. But the others are right there there is no way a woman could go to school in Oxford. And shipping fo and from the States was embargoed for a few years around the 1812 war. 

The sailing ship would take up to 2 months for the journey. 

She would travel by ship.  But if by ‘school’ you mean Oxford University, it did not admit female students at that time.  The first women’s colleges were estabilised in the 1870s,but the university did not recognise them officially until 1927.  

Sure, but such travel would have been difficult, and expensive.  And, unlikely in 1812!