How do we negotiate after survey?

[ToBeClear]

So we had an offer accepted on a house and our survey has come back with things that they recommend need to be fixed, and a valuation lower than the amount we offered (not significantly but more than £10k). How do we begin negotiations with the vendor? Through our solicitor or the estate agent? It all seems a bit odd here, having no one to represent us, the buyers...in the US both parties have representatives. We are totally unfamiliar with the process here as it's 20 years since we bought here! Thanks!

A house on a road popular with students does have a value. And if a buyer is prepared to pay x for it, then that is it’s vslue?

I agree that surveyors take emotion out and give a fair market value.
Location, square footage, condition, saleability.. gives market value

Well we went back to them with a new offer of £397,500. We shared the survey report with them indicating the valuation and the concerns over resale. The key issue is planning is no longer available for multi occupancy homes so as of now it can only be sold to a family or single resident. We'd be relying on resale to a family like ourselves who don't mind students. We quite like busy areas where we get a new set of neighbors every year lol. The vendor isn't stupid and knows he will have trouble finding another buyer right now, and even if he does a survey and valuation may come back even lower as we move towards Brexit. We're not quibbling over much but he may have his mind set on a figure beginning with 4. He wants a quick sale though and is walking away with cash as he's already bought his new home. We're prepared to lose it as we feel we're being totally reasonable. Why pay for a survey and then not act on it!?