Funding for grad school?

Sure. The way you put it you should have no problem, especially with the masters background. Don't just tell the graduate committee how you plan to be a scholar at their university, show them. When (not if) you land an interview or candidate interview show the graduate committee what you have learned through your master's program. Hopefully your master's was a thesis based due to the shear backup power on knowledge you will have, and tell them how you are going to use what you have learned and performed scholastically to the next level. If you are going in for your Ph.D. really think about how you are going tell them the directions you are heading or plan to head. If you have had the opportunity in working on a thesis tell the committees how you are committed to academic excellence in your field and specialty. Tell them something that isn't a cookie cutter version of every other student that has passed in front of them, most importantly express interest in the program but don't be too over zealous. Make sure you are relaxed, ask questions and most importantly, if you get to go to the UK before you apply, talk to faculty in the area(s) you are looking into. Get to know them and talk to them on a regular basis. If you can't go to the UK in the short term, write to the faculty members of the program of interest. Clear communication and a strong, developed candidates make the best graduate students.