I’ve booked and paid for my holiday arrangements. Can my travel company still request a surcharge?

Yes, as long as their booking conditions allow them to surcharge and don't say that no increases will be made after the booking is made - a no-surcharge guarantee.

Surcharges shouldn't be confused with additional charges that you may incur for changes to your booking such as amendments or additional services. These charges will be set out in the booking conditions.

If you have booked a package holiday, surcharges can only be levied when the cost of a package holiday goes up after you booked because of currency fluctuations (the euro growing stronger against the pound, for instance), rising fuel costs (e.g. for flights and cruises) and taxes. No surcharges can be passed on within 20 days of the departure date of a package holiday. If the surcharge is more than 8% of the total cost of your package holiday, the holiday company must offer you the option of cancelling and getting a refund.