If you satisfy some criteria, you might even be allowed to settle in Britain without refugee status, although it would help your case a great deal. In your original post, you mentioned college and graduation. Having educational qualifications could also help in persuading the British authorities to rule in your favour.
However, if you claim asylum as a refugee, have a good explanation ready if a British case worker asks why, if you were in danger, you waited until graduation before seeking asylum. You might, for instance, explain that you were living in constant fear of discovery, but thought it best to continue your studies until you and your boyfriend had enough money and information for you to travel to Britain.
As a "Newbie", I might not yet be allowed to link to external websites, but if you do a Google search with the words "UK Visas and Immigration -
GOV.UK", you will see a British Government web page with that heading and a
gov.uk extension. (I suggest that for now, you ignore the immigration lawyers ad that displays before the
gov.uk website. They might cost a great deal of money if you ask them to help.)
On the "UK Visas and Immigration -
GOV.UK" web page, you will see a number of helpful links, including "Visas, asylum and sponsorship" (which gives more information about seeking asylum as a refugee), "Settle in the UK" and "Immigration Rules". I suggest that you and your boyfriend study the information on that website.
I will just show two important quotations from the website, about the asylum process:
"You must apply for asylum if you want to stay in the UK as a refugee.
To be eligible you must have left your country and be unable to go back because you fear persecution."
and
"You should apply when you arrive in the UK or as soon as you think it would be unsafe for you to return to your own country. Your application is more likely to be denied if you wait."
I hope that helps.