Hi G1ggle. I will keep everything crossed that this all works out for you. Do keep us posted!
Lilmiss. Absolutely you should be looking at houses priced 20k higher than your budget. (Unless you're looking at very low priced houses of course, or ones you know have been reduced or are already realistically priced) It makes perfect sense to do so, especially nowadays when many houses are so wildly overpriced. Personally, in the bracket we're looking at we have been looking up to 50k higher, possibly more if we knew a house was overpriced & tracked these properties to see how long they'd been on for & what interest they had, any reductions etc. I really know my market & have been tracking obsessively for about 2 years now. 
The main problem nowadays is that most people haven't bothered to do their research & don't know the market at all, or they think that a quick look at recently sold prices & putting 2 & 2 together & making 5, or Zoopla estimated values, (which are so easily manipulated, I don't suggest anyone takes seriously) is enough to give them the information they need. They also take greedy EA valuations seriously, who are still working on 2 years ago's figures & adding a bit on to win the client & bump up their figures with the intention of getting their vendor to reduce at a later date. This leaves a huge amount of overpriced property on the market which nobody is prepared to pay for.
Then there's the people like myself, who have bought & sold many times, who do know the market & don't want to faff about, so price to sell to start with, but still expecting a reduction in the current market, finding that viewers, haven't done their homework & are tarring everyone with the same brush. We are also having the clear problem where most vendors simply don't get it yet that the EA have overpriced them to get their business, hence unless we get a buyer soon for ours we won't have anything else to look at because of the overpricing.
The key is to find a chain of people all willing to reduce down accordingly & then at the end of the day everyone is a winner.. except heres where the FTB comes in. They have done their homework & know the market is dead they hold all the cards, so they, quite rightly so, are looking to get a bargain! Im all for it & VERY realistic about pricing. More than most tbh, but there is a limit as to how much anyone can be expected to reduce down in order to move on.
I really should take my own advice, because I have done this many times before. It is hurtful when someone is rude or makes an insulting offer. But these people are merely trying their luck. I was super offended when I got offered 160k for a house id paid 195k for only a few years earlier. It wasn't a realistic offer, it was a punt. Eventually I got 190k (which still hurt, but it was a shit market, & I had dropped the vendors 20k when Id bought it so alls fair etc)
The key is to hold your nerve & everything will come good in the end. Rinse & repeat! That is our motto here ladies!