I was in this situation (sort of) last year, where I accepted an offer on my house, and, once I knew what was available money wise, found a house to buy. However the people whose house I was buying seemed in no hurry to complete (hassles waiting for them to let the survey be done, left waiting for them to respond to solicitors letters and phone calls). I wouldn't have minded so much for the fact that they were moving to rented rather than buying, and that it was them who needed to sell rather than me needing to buy that particular house.
To cut a long story short, I contacted their agent many times about these delays, and got nowhere until I gave them notice that unless I had some positive feedback of when I was likely to move, I was withdrawing the offer to buy. That did work.