Sorry, I couldn't resist...
Joking aside, bridging loans (which were always ridiculously expensive) have largely gone the way of the dodo.
However, I think you are looking at this the wrong way. If I was you, I'd identify the house you want to buy, take out biggest mortgage you possibly can with EBS and close the sale in the ordinary course (making sure you pocket 2% of the amount borrowed as per their current offer). Then sell your current house and use the proceeds, together with the balance of your savings, to pay off the mortgage ASAP.
Effectively you get to buy your new house at a discount!
It's nuts but that's the way our banks want to do business at the moment.
Meanwhile, our esteemed Central Bank wants banks to produce meaningless policy statements on how they price variable mortgage rates.