I have just moved house so I can appreciate the problem. First things first though, DO NOT GO OVERBOARD AND PUT A DEPOSIT ON THE HOUSE YOU FANCY(sorry about the shouting).
One cannot rely on other peoples word because there are always other factors that happen. For example, I reached an agreement to buy my present property because the vendor said that they were going to move in with(funnily enough) their in-laws. Not long afterwards they saw a property they liked and put in an offer and all of a sudden there was a chain that originally had 2 below me and one above and now suddenly had 2 other people with complications.
The only safe way is to sell your property on the basis that you will move out into temporary accommodation. Bear in mind that you may not actually have to do this but should prepare for it. You see ,just like in my case ,the vendors of the property you fancy will probably see a property that they fancy and so it goes on.
By selling and moving out(if necessary) you will break the chain and this will put you in a powerful position as a cash!!! buyer. There is also the fact that the pro rata interest that you earn on the capital you get for your property will more that pay for removal and temp.dwelling.
Now, if you need to carry over a mortgage etc make sure first before you do anything that you have the appropriate guarantees in place. Many purchasers will tell you that they have all their finances in place when all they have had are suggestions. Make your Estate Agent earn their money by bringing only clients that seem to be in a position to purchase.
Should you not get this house you fancy don't worry because, believe me, something else will be out there just as good.
Hope this helps.