We resited the kitchen at our last house, which was unmortgageable when we bought it as the old kitchen - in a 1980s annex - had been removed by the previous owner. We considered knocking down the annex internal walls and keeping the kitchen at that end of the house (eventually we did knock those walls down, but utilised the space for a different purpose), but realised that wouldn't work best for us. Instead we tacked a large vaulted ceiling kitchen extension onto a reception room at the opposite end of the building. This entailed taking down an old attached, stone outbuilding and temporarily removing the boiler that the PO had had fitted in this delapidated and badly leaking space a couple of years previously 
Our costs were high because - despite doing much of the donkey work ourselves - we had an architect design the space that involved stupidly expensive double height windows and we used high end finishes (limestone, granite etc), plus the whole house (200 years old and thatched) needed rewiring too.
So basically it involved rerouting plumbing, electrics, drains etc to the new kitchen - no gas in the village, we were on oil - and all sorts of shenanigans with trying to conceal wiring etc in a house where the ceiling formed the floor of the room above......happy days!
We're about to embark on a slightly less ambitious or so I stupidly thought resiting of the kitchen in our latest house - moving the kitchen across the hall to a reception room with the old kitchen becoming a utility. Our biggest problem here is that the house is built into an escarpment and the ground floor rooms - not to mention the cellar obviously - are semi-basement with the side we wanted to position the sink being underground. We also have a 1920s parquet floor we don't want to remove to lay pipework, so instead we've decided to have the sink on the opposite side where there is existing plumbing (bathroom above) and a drain immediately outside the nearby door.
Even so - and with DH doing as much of the work as poss himself - it won't be cheap.
In a flat I would have thought it would be a considerably simpler process, although having said that, we're currently helping DS rejig stuff in the kitchen of his flat (share of freehold) that involved knocking down a non-load bearing wall and that has unearthed all sorts of issues with ancient wiring in the ceiling and badly bodged plumbing from when the place was converted (1980s?). It's kind of hard to say till you start work and start discovering unexpected problems - what started out as a two week job is now looking like 3-4.
You need to weigh up whether it's logistically feasible and also financially worthwhile. Could you get a couple of builders round to give you quotes before you exchange?