Hey how old are your kids? One way to find a good English teacher in Hong Kong is to hire an agent. This is the best option for lower income families as the agent rates are significantly cheaper. The tutor fees could vary from HK$ 300-400.
Do make sure you check the authenticity of the tutors. They should be experienced and should have the right qualification. If you need a supervisor or someone to help with the daily homework; a per hour charge of $200 is enough. A qualified teacher might charge higher. So be thorough and check.
Based on experience, I would suggest the best would be to ask help from teachers at the local school which your kid attends. Some of the financially good families go for expert tutors available at higher rates. The middle income groups can consult coaching or cram schools for some help in getting a good english teacher available for private or home tutoring.
What are the improvement areas you are looking at? Do your kids need an expert advice on phrases, sentences, verbs, grammar, pronunciation because that would require an expert and yes as said earlier charges would be higher. Additionally, you could encourage your kids to make some english speaking friends in the neighborhood, or let them watch some English programmes for familiarity with the language and pronunciation.