One IDP will be required for each country you will be driving through. The good news is that IDPs aren't overly expensive, at only £5.50 per IDP. It is not yet known if a UK citizen hiring a vehicle abroad would require to pre-purchase an IDP, however you may want to check with your rental company before you travel.
The application process for IDPs are less than 10 minutes, and they can be bought from your local Post Office, or via
https://www.postoffice.co.uk/identity/international-driving-permit
IDPs also seem relatively easy to buy, however from 1st February 2019 they will only be sold via the Post Office. The process is a quick 5-minute transaction, you can simply walk in without an appointment or pre-order and ask at the counter.
See more information on IDPs and which one could be right for you here (https://www.gov.uk/guidance/driving-in-the-eu-after-brexit-international-driving-permits#driving-in-the-eu-and-eea)
You will also need to acquire a
Green Card for your specific dates of travel. This is a physical card, acting as a certificate for your vehicle insurance and is provided by your insurance provider, or third-parties within the UK. A Green Cards will be needed for driving within the EEA (European Economic Area) and some additional countries, including Andorra and Switzerland. A full list of EEA countries is available here:
https://www.gov.uk/eu-eea
As we are still not 100% certain on what will happen come departure day, it is advised to take all additional motoring documents with you as they could be requested at the departure/arrival borders discretion. Green Cards are available as PDF downloads, generally within 24hours, however if you require a physical copy please allow 3 weeks before travel for it to arrive.
Also, it is worth mentioning that even if you are driving, flying or swimming to Europe, Passports will need to be valid for at least 3 months from the return date. Motorists will also need to take their V5C Log Book (this is generally found in your glove-compartment or boot), as well as GB sticker. If you are hiring a vehicle abroad, you will not need either of these. See more on Gov
https://www.gov.uk/visit-europe-brexit