Why is there a call-out charge?
Call-out charges are grossly misunderstood by many customers and unfairly despised by most. People often don't appreciate that if you book an engineer to call at your house, the engineer has to allow for between half an hour and up to an hour's slot in his day to fix your washing machine. If he only books in 5-6 jobs each day then one sixth of his day is given to you. Once he has a full day's work booked in, he could lose work when other customers can't be fitted in. If subsequently he comes to your house and you aren't even there, or you don't have the repair done, then it has cost him much more than the cost of the petrol to get there.
People tend to unfairly resent paying call-out charges (in the same way they resent paying delivery charges after buying a product.) These resentments are understandable to a point but unfair. It costs money to call out to a customer so of course they should pay. Many engineers realise that customers are generally much happier when call-out (and likewise delivery charges) are simply hidden within the cost of a product or service, but it you do not have your appliance repaired it's not possible for an engineer to hide the costs unless they charge extra on successful repairs to cover it.
If a call-out charge is very high then it's a different matter, but a small £30 - £40 charge is very reasonable and even £40-£50 will only cover the actual costs of sending some engineers to a customer when a company employs engineers.
An important note, often not appreciated, is that if an engineer has a call-out charge, then their labour charges are likely to be reduced accordingly, they are not additional charges. It's highly unlikely that a company charging £40-£50 call out would also charge as much for labour as another company offering no call out charge. They are most likely just splitting the costs in order to cover the costs of coming out if you don't have the repair done. Conversely, someone who doesn't charge a call-out charge may well quote and charge more for the repair to cover it. So ironically, you could pay more for a repair from someone not charging for call outs. e.g. One company may charge £45 call out and £60 for the first hour or part of. Another company may charge NO call out, but charge £55 for half hour segments - £10 more.
The moral is to find out exactly what all the charges are before an engineer is booked.