To achieve the "tile inside and out" you would have to work with an "indoor/outdoor tile". This will increase the cost of the tile a bit. It is a nice "option" if you always have a set of french doors open during the summer time. If not (you don't have french doors or you rarely have them open) the extra cost of working with the indoor/outdoor tiles may not be worth it for you.

London is not considered a 'warm' climate so I would hesitate to put in a cold floor such as tile. Wood, in Canada and other cool/cold climate areas, is far more acceptable/easier to live with once the summer temperatures disappear. Engineered hardwood is a great option for London (humidity). It will require a bit more maintenance but a dirty floor is a dirty floor. Tile or wood would still require cleaning once dirt is on it.

I've lived in Germany and most homes had wood of some sort...leading right out into a garden. The few areas that had tile were FREEZING...even in the short, temperate summer time I couldn't go barefoot. I was in Frankfurt...so the summers/winters were not much different from London weather.

If you have underfloor heating I would go with the tile! Some of the new wood effect tiles are much nicer that actual wood now! But if you don't have underfloor heating I would go with wood, specially if it's an old house that wouldn't have as good insulation underfloor! The house I'm living in at the moment while my house is been built has tile in the kitchen and bathrooms and my 4yr old daughter makes me lift her over the the toilet if she doesn't have socks on...Baltic!!!
The house I'm building is going to have underfloor heating on the ground floor and I'm going to have a wood effect tile running the whole way from the entrance Hall to the kitchen come family room which also opens out on to the patio. My mother has normal tiles and underfloor heating and my daughter is always lying down on the floor to play so I have no worries about it feeling cold! Hope this helps

Oh and sorry I'm in Ireland, Donegal