No actually. A basic ceremony costs around £57, although this can vary depending on which part of the country you are, as the rate is set by the council. This would not include the cost of the ceremony room which you'd only have if you wanted a bigger event at that time. The other fees include the fee to give notice, which is £35 per person. Any additional marriage certificates start at about £10 and admin costs about £10. Having a Celebrant led wedding doesn't mean you pay out twice- in fact it can work out the same or less expensive. You don't have to book a licensed venue which will save money or pay for the registrar to come to you.
To give you an idea of costings, take a look at this useful page from Bridebook.
https://bridebook.com/uk/article/how-much-does-a-registry-office-wedding-cost
● Monday to Friday (office hours) – £300-400
● Monday to Friday (outside of office hours) – £400-£450
● Saturday – £500
● Sunday – £550
● Bank Holiday – £525
● Special Days (for example, Valentine’s Day, Christmas Eve, New Year’s Eve, New Year Day) – £600-£650
You may also have extra costs added on - musicians, decorations. So as you can see, a celebrant wedding is not really any more money and you get SO much more for it.