We could find only three well known hotel booking web sites, Hotels.com (hotels.com from Ireland) (hotels.com from UK), Hotelopia.com & Agoda.com) that allow customers to currently book hotels using PayPal. Superbreak is a UK based holiday company that specialises in UK hotel short breaks. But they also offer a good range of hotel offers throughout the world. Hotels.com is a well recognised brand in the hotel booking sector.
Update 8th September 2017. Hotelopia.com now also accept Paypal for bookings at their site. The Paypal logo is displayed at the bottom of their home page.
(Hotels.com from Ireland) (Hotels.com from UK)
Hotels.com allow online booking with MasterCard, Visa, American Express, Diners Club, Discover credit cards, Visa Electron, and also Paypal as a payment option. There is a UK and Ireland site for Euro and GBP.
Agoda is a hotel booking site that offers hotels worldwide. Agoda lists hundreds of thousands of hotels with services and since 2007 is owned by Priceline. Agoda currently allows customers to book hotels using Paypal as a payment option. Simply select Paypal as a payment option during the booking process.(Paypal option confirmed by visit September 2017 - given as payment option in FAQ page)
Toprooms.com offers a range of independent hotel and B&B accommodation in the United Kingdom. Online bookings with Paypal are possible.
In general, all other major hotel booking sites require that you use a credit card to make a hotel reservation. Many do not charge your card until you have completed your stay. But depending on the cancellation policies, hotels will apply a no-show charge to your credit card if you fail to turn up at the hotel.
If you do not wish to use a credit card, debit card or PayPal account for hotel bookings, then your only other option may be to contact the hotel directly. You may be able to work out some other arrangement that will satisfy the hotel's requirements.