Hi hm88,
From what i googled, EYFS is not exactly a 'teaching method', but a set of welfare and learning/development requirements which must be followed by childcare providers required by the UK government (parents please correct me if i'm wrong). Most kindergartens do have a more structured learning environment with children born in the same year range. I'm guessing that if you are planning to send your child to a UK school (here in hk or uk in the future), then i think schools that follow the EYFS would be suitable for your family.
Kids taught with the Montessori method are encouraged to be more independent and use self control/self direction, instead of having a teacher dictate to an entire class most of the time, but the environment is highly structured and require more discipline in certain ways (My son has been to both so i know). However any school can be use/claim to use the Montessori method, so it is best to look at each school individually and make sure you like what they're teaching how they are teaching it. Some schools like Woodlands do incorporate Montessori but also cater for transition into 'regular' schools, so you can ask the schools you are looking into about any transitional provision into future Primary education.