My housing association landlord is trying to insist on fitting a fire door to the kitchen, the problem is they are refusing to match it up to the style of all my other doors which I have installed at my own cost,

I live in a self contained 2nd floor flat.

Do they have the law on their side to insist that I must comply. 

The style of door is not a fire safety matter you can get fire doors on many different styles. However, do you need a fire door to your kitchen, is a fire safety matter but without knowing the layout of the flat it is impossible to give a definitive response. Fire safety in flats is subject to the Building Regulations and guidance is contained in Approved Document B (Fire Safety) Vol 2 Section 2 page 21 covers the layout of flats and you need to study this section to understand if a fire door to the kitchen is required and if it is then a fire door has to be fitted but the style is another matter.