Its certainly do-able for £400. A wi-fi router won't cost much, about £20 upwards for one these days, depending on the features. The real hassle is setting it up.
You will be able to find lots in the 15" section but not many that will be on XP. Times change and although people still like XP, its number is up, and to be honest I have Vista and really like it. Its more future proof than XP if nothing else.
What sort of things will she be using it for? It would be helpful to know as it will give us an idea of the necessary specs. At 65, I could be wrong but I doubt she will be gaming on it! If it is just surfing the internet and basic stuff like Office and such, you don't need to break to get one that will do the job.