Pop along to your local births deaths and marriages building. You should be able to find out there. The legislation changed a couple of years ago to protect identity theft so be prepared to pay.
if it was between 1984 - 2004 then you can go on
www.ancestry.co.uk
click on go directly to birth/marriages/deaths
scroll down to the bottom of the page and click on deaths under the sub heading of complete bmd index 1984 - 2004
put in the details you have and the name will come up automatically without you having to go through anything
if it doesnt come up you can take it they're not deceased as it is quite comprehensive
If it is more recent than Ancestry will have (ie after 2004) you could try the local paper. I know my local paper has 'Family Announcements', including deaths, online.