Something I learned about FedEx a few days ago is that they will only cover collectibles up to $1,000 in value (see here). With FedEx you’d need additional insurance, which FedEx themselves do not offer. UPS on the other hand will cover collectibles up to £50,000 in the UK and $100,000 in the US, and it’s entirely based on the declared value of the package.
As for Royal Mail, make sure to ask for insurance if you’re sending items between £500 and £2,500 in value. Special Delivery orders are covered up to £500, but after that you won’t get any more back unless you ask for additional insurance (which only costs around £3). Royal Mail do not offer insurance above £2,500.