Firstly, welcome to the tricky world of children education... It is a minefield I find
Having said that, I dont think your child will be at a disadvantage either way. Honeywell is a very good place to put your children in as well as is Mouse Hole. There are some indenpendant schools that assess the children like Thomas' and they know the nursery schools around. Mouse Hole is one of them so if you plan to send your child there going to Mouse Hole would probably give you a better chance. There are some parents that are very strategic and are better placed to give you an opinion on which order, which nursery schools to apply to if that the way you want to be.
My opinion is that you should put your child in the place where you think he will be the happiest. Because as you said, if a child is happy he/she will learn. I am not strategic when it comes to those things as I really want to find the place where I know my child will thrive because it fits my child personality, needs, etc. But you do have to plan ahead as there are loads of places with very long waiting lists.
The other thing to consider is that 2 is not too young to learn to sit and to concentrate for a short period of time. The earlier you start the learning process on that, the better. it can be done by sitting on the carpet to listen to a story, or drawing for 5min, etc.
Montessori is about children leading the pace at which to learn rather than somebody telling them how and how fast they should learn, it is about learning whilst playing, and there is a more natural way of learning. Dont be put of by the name. At Mouse Hole, and others, there is a structure (to give them a sense of school) but it is not academic far from it. They are all children having fun there (and they learn).
Good luck into finding your way