Flower prices have been rising for a few years and have skyrocketed in the last few months thanks to Brexit and Covid. The consumer gets very confused about flower pricing because the supermarkets sell flowers so cheaply but there is no comparison in terms of quality. It's like comparing Tesco Value burgers with organic fillet steak.
Although there aren't many items on your list, some of them will need A LOT of flowers and foliage (i.e. signing table, arch and barrel arrangements. I'm literally talking buckets and buckets of flowers.
What flowers did you ask for? Were you very specific? Roses, peonies, hydrangeas and eucalyptus are very popular for summer weddings but they are expensive! Directing the florist to images on Instagram and Pinterest is also dangerous. Flower arches alone can easily cost £500+. The problem that florists have is that they're not really sure of the cost price of your flowers until they order them so they have to factor that in when quoting. The market is driven by demand so if a flower is in high demand on the day it will be reflected in the price. The retail price of some red roses was £5.50 per stem yesterday.....
If you want to reduce your quote, I suggest the following:-
Don't be specific about particular flowers
Identify the 'style' of flowers you want (i.e. English Country Garden, Tropical, twiggy and rustic, etc.)
Choose the colours (i.e. pastels, white and green, pinks and reds, etc.)
Focus your budget on the flowers that will appear in your photos (i.e. bridal) and those the ones your guests will be looking at (i.e. table centres, a large vase arrangement for the church/reception). A flower arch will look lovely but you'll only be under it for a few minutes while you have photos done so it's not actually very good value!
A good way to maximise your budget is to give an arrangement two jobs so a large vase arrangement in the church could be moved to the reception. You're then getting the benefit of it all day. I saw a florist recently who made the milk churn arrangements as handtieds. Later in the day, they were wrapped and presented to the Mums as handtied bouquets which is a great idea.
Don't be afraid to go back to a florist and ask them what they suggest in terms of reducing the quote. If they're good, they should be able to come up with some suggestions. It's all about where you focus your spend. There are some awesome florists posting pictures on Instagram but loads of them are easily £150 for a bridal bouquet territory because their bouquets are full and overflowing. Unfortunately, if something looks expensive it generally is expensive hence the reason why your Nanna likes Xants!.