How long have those houses been on the market?
It's hard to generalise. One of my DD's bought a property just outside the M25, not London. There was a huge demand for the good properties and many went for the asking price (these are 2-bed flats.)
Those that were slightly dodgy hung around for months and still didn't sell.
So much depends on the vendor's circs. If there is a chain and they need a quick sale they are likely to accept a lower offer.
Have you and her researched Right Move and the sold prices in the same road? Or similar?
Obviously the vendors will have done the same.
A 10% reduction on £340K is quite a low offer if the flat is priced correctly.
Based on our experience, and the flat was less than that, people were offering within £2k-£5k below AP.
So on £260K they would offer £255, or even £258.
I think you need to establish if the flats are overpriced, or your DD is being unrealistic over what she can afford. Maybe her real budget is a 1-bed?