I would recommend Ian Day Decorators: http://iandaydecorator.co.uk/
We had our house renovated and redecorated last year and the decorating costs without colour paints (white included) were around £7k.
Now, ours is a smaller space than yours - 2 bed Edwardian terrace with a loft conversion adding 2 more bedrooms and another bathroom.
You definitely want a decorator rather than using a company that does everything as I saw what went into achieving that professional finish.
5 beds over 3 storeys, if you're including some bathroom paint work, doors, skirtings, hallways, living room, dining room, kitchen etc. I wouldn't be surprised at £10k but £16k sounds pretty high.