Good luck Luckygirl.
It's all so difficult isn't it, people tell lies and the EA have a hard job to prove they are proceedable. My first buyer said he was in rented and had cash - he wasn't, he lived in a £750K house which he still had to sell, wasn't even under offer. I'd jumped through hoops to accommodate him, my son took a day off work for his second viewing as I was away visiting my aunt, I was furious. He withdrew once the EA proved he didn't have the funds. Second EA had to pursue my 'cash' buyer for three weeks to prove his funds, it turned out his ex wife in Sweden had the cash, he wasn't getting any of it, he withdrew.
I wouldn't come off the market until the person can prove their funds.