There are 33 countries that are given the same on arrival free UAE visa on arrival similar to UK citizens.
These countries include citizens of France, Italy, Germany, the Netherlands, Belgium, Luxembourg, Switzerland, Austria, Sweden, Norway, Denmark, Portugal, Ireland, Greece, Cyprus, Finland, Malta, Spain, Monaco, Vatican City, Iceland, Andorra, San Marino, Liechtenstein, United States (US), Canada, Australia, New Zealand, Japan, Brunei, Singapore, Malaysia and Hong Kong.
A new law was passed on March 31st 2003, where the citizens of these 33 countries can only obtain a one-month non-renewable visit visa on arrival, which costs Dhs. 100 (US$ 28). Though the government officially passed this law, it does not seem to be always implemented.
Haven't heard of anybody paying for it lately.
Full link here;
UAE Visit/Tourist Visa Requirements [United Arab Emirates] - TEN Guide