In many (probably most) countries throughout the world, it's standard practice for prices for goods and services to be quoted exclusive of taxes. (For example, hotel prices in the USA normally need to have both state and local taxes added onto them. Similarly, restaurants in many European countries advertise prices which exclude their equivalent of VAT).
The UK is different in that the prices goods and services which are generally not supplied to other VAT-registered businesses (e.g. prices in High Street shops) must include VAT. However it's still perfectly normal practice for businesses like garages to provide quotes which exclude VAT. (If a garage says that they'll fix your car for a certain price you should ALWAYS assume that VAT will be added to the price, unless specifically stated otherwise). Similarly businesses which provide many of their products or services to other businesses will nearly always quote prices which exclude VAT. (Staples, the office stationers, used to have all of their shelf labels displaying non-VAT prices. It was perfectly legal but it would have been illegal for, say, Tesco to do the same with their stationery products at the same time).
If I'd got that quote from a tree surgeon it would never have occurred to me not to add VAT to the total, as this is standard practice with such businesses. You haven't got a leg to stand on; you still owe £90.
Chris