The internet is awash with people giving incorrect advice regarding charges by private parking companies, so let me take this opportunity to set out the actual law.
When you enter a car park, you trigger the start of the consideration period. This must be at least 5 minutes in most cases, but for most large car parks (more than 500 spaces) offering free parking for one hour or more it must be at least 10 minutes. At the other end of the scale, there is no consideration period at all for pre-booked parking and the consideration period is only 1 minute for some short stay parking such as airport drop off areas. The consideration period is not free parking. It is intended to allow you to decide whether to park, including finding an empty space and checking the terms. If you park and leave the premises or remain stationary for 5 minutes, the consideration period is over, so if you park, pop into a shop to buy something, get back to your car and leave, the operator can charge you even if that has taken less than 5 minutes. If your car remains in the car park after the consideration period has expired, you must pay. Unless it is a pay on exit car park or the signage specifically states that you can pay at any point during your stay, you must pay before the consideration period expires. Arguments about only being a minute or two over the consideration period will not get you anywhere. The only way you could successfully argue for longer is if the consideration period is too short to allow you to park and pay, e.g. the only way the parking operator allows you to pay is via a smartphone app but there is no signal in the car park.
If you have paid for a fixed period of parking, there is a grace period of at least 10 minutes for most car parks. The main exception is some short stay parking such as airport drop off areas, where there is no grace period. The purpose of the grace period is to allow for unexpected delays. As with the consideration period, arguments about only being a minute or two over the grace period will not get you anywhere. The only situation I can think of where you could successfully argue for longer would be at a pay on exit car park where the time allowed was insufficient to get from the payment machine to your car and exit the car park.
Some people think that whether the parking company or the owner of the land has suffered a financial loss is significant. It is not. Imagine a car park offering 2 hours free parking. The signs clearly state that you will be charged £85 if you overstay. When you arrive, the car park is half empty. You stay nearly 3 hours. The car park is still half empty when you leave. Clearly, no-one has suffered a financial loss due to you overstaying, nor has anyone been prevented from parking. However, you receive an invoice from the parking company for £85. Would the courts uphold that?
What I have just described is what happened to Barry Beavis. The parking company involved was ParkingEye. He ignored the invoice and the subsequent reminder and warning letter. The case went to court. Beavis lost. He appealed. He lost again in the Court of Appeal. He then appealed to the Supreme Court, where he lost again. The Supreme Court was clear that the fact ParkingEye had not suffered a financial loss was irrelevant. They held that the charge was a reasonable means of achieving two legitimate aims - to deter long stay parking that would reduce the availability of parking spaces to shoppers, and to provide an income stream to ParkingEye to meet the costs of operating the car park and allow them to make a profit.
Parking companies know that, if they take you to court, they will win unless you can show that the signage was inadequate, the payment machines were faulty or there were mitigating circumstances such as breaking down. And, since the law changed to allow them to pursue the registered keeper of the car, they no longer need to identify the driver. That is why there has been such a huge rise in parking companies taking drivers to court. Some parking companies are more litigious than others. ParkingEye are one of the most litigious. But, regardless of the company involved, it is no longer safe to ignore charges from parking companies or assume they will go away if you appeal.