Belgium are part of the EU, so yes they could:
As a national of a European Economic Area (EEA) or European Union (EU) country, you have the right to work in any other member state, without the need of a work permit. You will also have the same rights as nationals of your destination country in working conditions, pay and social security matters.
Not all qualifications are recognised across the EU and EEA, and some professions have employment restrictions. You will be able to check your qualifications against occupation information sheets produced by EU member states, which will allow you to see if your UK qualification is acceptable. Language skills and fluency levels may also be an issue when seeking work.