I cannot speak for the UK, however in the Untied States you can check with the Financial Aid Departments of the colleges you are looking into. There they will have a list of all the scholarships available particular to that school. You might also want to ask about the different corporate sector businesses. Many of them offer scholarships within designated areas.
The best way to get a study abroad scholarship is by having essays that impress examiners, of course along with other things like SoPs, LoRs,extracurricular but on first glance it is your essay. For this I would recommend you to check out Kenilworth Global Consulting. 90% of all its students have received a scholarship and a 98.2% of them a Visa.
You need to talk with your local univeristy about programs to come and study in the US. Then you need to fill out the proper forms.
USA High - 1997 Christian's Scholarship 2-14 was released on: USA: 29 March 1999
Generation Why - 2010 Scholarship 2-4 was released on: USA: 23 March 2011
High School Scholarship Quiz Bowl - 2011 Quiz Bowl Scholarship Time 1-10 was released on: USA: 13 November 2011
High School Scholarship Quiz Bowl - 2011 was released on: USA: 7 June 2011
D.c.
if you are eligible for merit scholarship. it is possible to get 3000usd.
Good Times - 1974 Thelma's Scholarship 2-23 was released on: USA: 11 March 1975
Meet the Browns - 2009 Meet the Scholarship 3-37 was released on: USA: 2 June 2010
Leave It to Beaver - 1957 Lumpy's Scholarship 6-24 was released on: USA: 7 March 1963
Mathematics Illuminated - 2008 The Primes - 1.1 was released on: USA: 6 May 2008