You have agreed to buy the vehicle and hence the deal to purchase will need to go through, but from what you have said there is no agreement to go through with the part exchange. What they have done is told you the book value on your vehicle, hence the part exchange is not part of the contract and you can sell it where you like. That said, any "valuation" made by a salesman at another garage is not necessarily what it is "worth" and the £2800 price is not likely to be an offer to purchase at that price but would be part of a wider deal. Take your car into the dealer and see what they will offer you for your car. By all means use the higher figure as a bargaining ploy, but check around for equivalent cars for sale and also with Glass's and Parker's before you refuse any trade-in price you are offered.