Generic domain names like DrummingLessons.co.uk, FurnitureRepairs.co.uk, PerfectDays.co.uk etc are valuable because they are meaningful and describe products/services in a familiar way using words that everyone associates with them.
(That's why you're here, reading this page...)
This makes them easy to remember without even thinking about it. People simply associate your domain with that product/service e.g to find your site again they may think, "I was looking for a Drumming Lessons... Ah yes, DrummingLessons.co.uk".
You'll save money when advertising/promoting your site as a generic name will be remembered/associated to that product/service after fewer interactions. It'll also make it easier to promote offline and help with word of mouth.
A generic domain name will also enhance the trust and credibility of your company which is an important factor every time a potential customer see's your URL, for example when browsing a list of search results to choose between competing company’s/offers.
If you use PPC advertising (like Google AdWords) it may benefit you by increasing the number of clicks you get as well as reducing the price you pay per click.
A generic domain name will help your search engine rankings, exact match domains rank much better in Google and other search engines.
Having a domain name that matches your main keywords will give you more attention on your search engine listing because both Google and Microsoft’s Bing show the words within your domain name that match the search term in bold (e.g. the search example below.
Finally generic domains will give you an unfair marketing advantage over your competitors. Since anyone can own them (first come, first served) once you buy the perfect generic domain name, none of your competitors will be able to get their hands on it.