The argument bit comes when they present an invoice for £5740+20%, and you pay them £5740.
There isn't any teeny-tiny print on the back of the quote stationery, saying all quotes are subject to their standard Ts&Cs is there? Because when you've found the Ts&Cs (behind the leopard or wherever), they probably do say quotes are ex VAT. I'd still view that as misleading though, if there's no mention of VAT on the face of the quote.