I am from Myanmar. I will be in Belgium on 3rd October till 30 October 2014. During my stay in Belgium, I would like to visit to London for three days. Is it easy and quick to get visa from Brussels? Or can we apply by online?
Based upon what you wrote, the governing authority is Paragraph 28 of the UK immigration rules. It states in part...
An applicant for an entry clearance must be outside the United Kingdom and Islands at the time of the application. An applicant for an entry clearance who is seeking entry as a visitor must apply to a post designated by the Secretary of State to accept applications for entry clearance for that purpose and from that category of applicant.
The UK has a designated post in Belgium that can accept entry clearance applications for VISITORS, and your category is 'Visitor'. It means yes, you can apply there.
You need to apply online and take your application to a Visa Application Centre.
For your other questions: is it quick and easy? It is easy, just complete the form online, print it out, and take it to a VAC. Is it quick? No, not in your case because you are a visa-national, which means your application will probably get referred to the Super Hub in Paris and they will have to get the consulate in Myanmar to look you up. You also need a full set of biometrics (even if you already did one) to accompany your application.